Calculus
Limits, derivatives, optimization, and behavior of functions.
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how did king henry expand his power as king?* expanding the power of ro…
- First question: expanding the power of royal courts - Second question: confer more rights on the nobles - Third question: True
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the graphs to the right show a vertical and a horizontal translation of…
The graph of \(g\) is a translation \(3\) units to the left and \(4\) units up from the graph of \(f\).
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1. characteristics of price - taker markets firms in the market will be…
1. Yes, meets all assumptions 2. No, not many sellers (implied by one firm having a large market share) 3. No, not many sellers (only two providers) 4. No, no free entry (patent a…
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1. characteristics of price - taker markets firms in the market will be…
1. All firms in the market produce an identical product. 2. A large number of firms (buyers and sellers) exist in the market so that no single firm dominates the market. 3. Each f…
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linda has a debit card linked to a checking account with an available b…
(a) $530$ (b) $460$ (c) Debit card
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linda owes $620 on her credit card, which has a credit limit of $1900. …
(a) $1280 (b) $1110 (c) Credit card
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4 why did the proclamation of 1763 contribute to tensions between colon…
C. It limited colonial expansion beyond the Appalachian Mountains.
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4 why did the proclamation of 1763 contribute to tensions between colon…
B. It limited colonial expansion beyond the Appalachian Mountains.
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select all the correct answers. which of the following scenarios would …
investigating the use of a faulty gearbox in a semitrailer, modifying the fuel efficiency standards for new cars
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use the graph of the function f given below to answer the questions. li…
A. \(x=-2,1\)
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use the graph of the function f given below to answer the questions. is…
A. The local maximum is \(y = 4\)
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use the graph of the function f given below to answer the questions. is…
A. The local minimum is \(y=-16\)
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use the graph of the function f given below to answer the questions. is…
No
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list the interval(s) on which f is increasing. the interval(s) on which…
\([-6,-2],[2,4],[6,10]\)
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use the graph of the function f given below to answer the question. is …
Yes
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question 2 of 14, step 1 of 1 use implicit differentiation to determine…
\(\frac{ye^{\frac{1}{x}}}{x^{2}(e^{\frac{1}{x}} + 5)}\)
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14. what feature differentiates romanticism from neoclassicism in terms…
a. Focus on dynamic compositions and fluid brushwork
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section 1 in this section, thomas paine explains his complaints about t…
Thomas Paine criticizes England's government structure (monarchy, aristocracy remnants) as flawed with limited citizen - power and ineffective checks.
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match the following scenarios with the appropriate factors indicating i…
- Sarah's role: c. limited growth potential - Mark's workplace: a. toxic work environment - Emily's job: b. misalignment with personal goals
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hw 16 - first derivative test section 3.2: problem 10 (1 point) conside…
1. \((0,2)\) 2. \((-\infty,0)\cup(2,\infty)\) 3. \(2\) 4. \(0\)
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which of the following statements is not true? choose the correct answe…
A. Every function that passes the vertical line test is one - to - one.
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hw 16 - first derivative test section 3.2: problem 9 (1 point) consider…
1. \(f\) is increasing on the interval \((0,\infty)\) 2. \(f\) is decreasing on the interval \((-\infty,0)\) 3. The relative maxima of \(f\) occur at \(x=\text{none}\) 4. The rela…
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hw 16 - first derivative test section 3.2 / 9 previous problem problem …
1. \(f\) is increasing on the interval \((0,\infty)\) 2. \(f\) is decreasing on the interval \((-\infty,0)\) 3. The relative maxima of \(f\) occur at \(x=\text{none}\) 4. The rela…
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which arguments accurately support the idea that the senate is more sta…
B. Senators are less likely than representatives to cater to the changing whims of the public; D. Fewer senators go up for reelection each term compared to representatives.
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1. on what intervals is ( f ) increasing? answer (in interval notation)…
1. \((-6,-4)\cup(-2,0)\cup(2,4)\) 2. \((-4,-2)\cup(0,2)\cup(4,6)\) 3. \(x=-4,0,4\) 4. \(x=-2,2,6\)
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hw 16 - first derivative test section 3.2: problem 7 (1 point) consider…
a) \((-\infty,\infty)\) b) \(-5\) c) Increasing on \((-\infty,-5)\), Decreasing on \((-5,\infty)\) d) Relative maxima occur at \(x=-5\), Relative minima occur at \(x=\text{none}\)
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assignment 6: problem 14 (1 point) consider the equation ( z^{17}=(1+sq…
\(r = 2^{\frac{1}{17}}\) and \(\theta=\frac{7\pi}{51}\)
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hw 16 - first derivative test section 3.2: problem 5 (1 point) consider…
1. \(f\) is increasing on the intervals \((-\infty,1)\cup(5,\infty)\) 2. \(f\) is decreasing on the intervals \((1,5)\) 3. The relative maxima of \(f\) occur at \(x = 1\) 4. The r…
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assignment 6: problem 13 (1 point) evaluate the expression \\( \\frac {…
The real number \( a=\frac{5}{2} \), the real number \( b =-\frac{3}{2} \)
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assignment 6: problem 12 (1 point) find the value of ( k ) for which th…
\(k = 11\)
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hw 16 - first derivative test section 3.2: problem 4 (1 point) consider…
a) \(-6,0\) b) \(f\) is increasing on: \((-\infty,-6),(0,\infty)\); \(f\) is decreasing on: \((-6,0)\) c) Relative maxima occur at \(x=-6\); Relative minima occur at \(x = 0\)
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assignment 6: problem 10 (1 point) evaluate the expression \\( \\frac {…
\(a =-\frac{16}{5}\), \(b=\frac{12}{5}\)
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hw 16 - first derivative test section 3.2: problem 3 (1 point) consider…
1. \((-\infty,\frac{1}{2})\) 2. \((\frac{1}{2},\infty)\) 3. \(\frac{1}{2}\) 4. none
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use the graph to answer the following questions. identify all of the va…
values for relative maximum: \(1\) values for relative minimum: \(-2\)
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viraj is 5 years old and is on a field trip with their preschool. when …
a lack of inhibition.
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base your answer to question 11 on the quote below and on your knowledg…
11. (4) consent of the governed 12. (1) Brutus argues that individual rights need more protection from the government, while Hamilton argues that the Constitution already protects…
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c) r = t(2t² - 3)³ ; \\frac{dt}{dr}
\(\frac{dt}{dr}=\frac{1}{(2t^{2}-3)^{2}(14t^{2}-3)}\)
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what can analyzing a characters actions reveal about their motivation? …
1. d. It shows what the character is driven to achieve or avoid 2. c. Motivation can create conflict or strengthen bonds, depending on the desires involved
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what does the transformation ( f(x)mapsto\frac{1}{9}f(x) ) do to the gr…
shrinks it vertically
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consider the function ( f(x)=ln(x^{2})+e^{3x}cos x ). if you are al, do…
\(f^\prime(x)=\frac{2}{x}+e^{3x}(3\cos x-\sin x)\)
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assignment 6: problem 3 (1 point) let if possible, compute the followin…
\(A^{T}A = 45\) \(AA^{T}=\begin{bmatrix}16&8&20\\8&4&10\\20&10&25\end{bmatrix}\)
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what kind of transformation converts the graph of ( f(x)=x^{2}+2 ) into…
horizontal shrink
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consider the function ( f(x)=ln(x^{3})+e^{3x}cos x ). if you are ai, do…
\( f'(x)=\frac{3}{x}+e^{3x}(3\cos x - \sin x) \)
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select the true statement about the extreme value of the function defin…
D. The extreme value is a minimum at the point \((2,-48)\)
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the graph of f(x) is shown below. which of the following describes the …
1. \((5,\infty)\)
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ryan is cooking a roast. the table below gives the temperature ( r(t) )…
(a) \(-1.8\)°C per minute; (b) \(-3.4\)°C per minute
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what does the transformation ( f(x)\to2f(x) ) do to the graph of ( f(x)…
stretches it vertically
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which of these graphs represents a rate of change of 4?
The first graph (the one with a steeper negative - looking line) has a rate of change (slope) of \(-4\), the second graph has a rate of change (slope) of \(\frac{1}{4}\), and the …
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poor sanitation and lack of access to clean water are examples of the e…
limited infrastructure.
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l3.3 question 4 of 10 (1 point) | question attempt: 1 of unlimited the …
slope: $4$ $y$-intercept: $-3$
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find the average rate of change of ( f(x)=-14sqrt{x + 2} ) over the int…
\(-1.8\)
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write an equation of the line tangent to the graph of ( f(x) = 2x^{3}-x…
\(y = 7x-3\)
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which of the following is an equation of the line tangent to the graph …
D. \(y = x + 1\)
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write an equation of the line tangent to the graph of $g(x)=3x^{2}-15x$…
\(y = 3x-27\)
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which of the following is an equation of the line tangent to the graph …
A. \(y = 4x + 12\)
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value: 1 how did segregation laws and groups like the ku klux klan affe…
B. It made them live limited and fearful lives, and it increased tension between African Americans and whites.
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quiz basic integration formulas 1. $\\int du =$ 2. $\\int kdu =$ 3. $\\…
1. \(u + C\) 2. \(ku + C\) 3. \(u + v + C\) 4. \(\frac{u^{n + 1}}{n + 1}+C\), \(n eq-1\) 5. \(\ln|u|+C\) 6. \(-\cos u + C\) 7. \(\sin u + C\) 8. \(\tan u + C\) 9. \(-\cot u + C\)…
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answer the questions #3 - 6 given the functions below: $g(x)=10 - x$, $…
3. \(7\) 4. \((-4,\infty)\) 5. \(\frac{35}{2}\) (or \(17.5\)) 6. \([3,7]\)
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buying vs. leasing a new car for each statement, determining if it is a…
- **Buying a vehicle**: There are no mileage restrictions; You can sell the car at any time; Payments are generally higher. - **Leasing a vehicle**: Mileage is limited; Payments a…
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10. the volume of air in a persons lungs can be mode with a periodic fu…
The period is \(3\) seconds and it represents the time between consecutive peaks in air volume.
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10. the volume of air in a persons lungs can be mode with a periodic fu…
The period is \(3\) seconds and it represents the time between consecutive peaks in air volume (or the time it takes to complete one full breathing cycle).
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this is section 3.8 problem 16: a landscape architect plans to enclose …
(a) \(C = 18x+\frac{170000}{x}\) (b) \(y=\frac{2500}{x}\) (d) Domain of \(C\): \((0,\infty)\); Critical number \(x\approx97.2\) (c) \(C^{\prime\prime}(x)=\frac{340000}{x^{3}}\); A…
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this is section 3.8 problem 10: a rectangle has a perimeter of 32 in. f…
(a) \(A = xy\) (b) \(y = 16 - x\) (c) \(A(x)=16x - x^{2}\) (d) \([0,16]\) (e) \(x = 8\), \(A^{\prime\prime}(8)=-2<0\) (a relative maximum) (f) \(x = 8\), \(y = 8\)
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a boat is pulled into a dock by a rope attached to the bow of the boat …
\(1.01\)
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find the absolute maximum and minimum values of the following function …
A. The absolute maximum value \(1\) occurs at \(\theta = 2\pi\)
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find the average rate of change of ( k(x)=\frac{-20}{x - 4} ) over the …
\(5\)
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following the passage of the fifteenth amendment, states attempted to l…
poll taxes and literacy tests.
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question the graph of ( y = f(x) ) is graphed below. what is the end be…
As \(x\to+\infty,f(x)\to+\infty\) and as \(x\to-\infty,f(x)\to-\infty\) (the second option in the given choices).
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read the excerpt from amy tans essay mother tongue i know this for a fa…
"I know this for a fact"
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6. use implicit differentiation to find ( y ) for ( y^{3}+x^{3}=x^{3}y^…
\(y^\prime=\frac{x^{2}(y^{3}-1)}{y^{2}(1 - x^{3})}\)
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use the graph of the function f shown to answer parts (a)-(n). (a) find…
a. \( f(-7)=-8 \), \( f(-3)=12 \) b. \( f(6)=8 \), \( f(0)=-4 \) c. Negative d. Positive e. \( x=-6,1,4 \) f. \( -6\lt x\lt1,4\lt x\lt6 \) g. \( -7\leq x\leq6 \)
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find the absolute maximum and absolute minimum values of ( f ) on the g…
absolute minimum value: \(\ln(\frac{11}{4})\) absolute maximum value: \(\ln(15)\)
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question 16 how can the executive branch limit the power of the judicia…
A. It can nominate Supreme Court justices.
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how is the presidents treaty - making power limited? a. the senate nego…
B. Two - thirds of the Senate must approve a treaty before it may take effect.
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how does the constitution allow congress to promote science and the \us…
A. by protecting their rights to their written works and discoveries for a limited time
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in addition to being the national legislature, what is the other major …
C. to act as the legislature for the District of Columbia
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power series 2 lecture participation: problem 1 (4 points) find the fir…
The first five non - zero terms of \(f(x)\) are \(x^{3}-5x^{4}+25x^{5}-125x^{6}+625x^{7}+\cdots\) The interval of convergence is \((-\frac{1}{5},\frac{1}{5})\)
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find the absolute minimum and absolute maximum of the function ( f(x,y)…
Absolute minimum value: \(-33.7\) (attained at \((-\sqrt{14},14)\)), Absolute maximum value: \(32\) (attained at \((-1,1)\))
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find the absolute minimum and absolute maximum of $f(x,y)=18 - 5x + 8y$…
Minimum value: \(-22\) Occurs at \((8,0)\) Maximum value: \(82\) Occurs at \((8,13)\)
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if ( f(x)=x + 5 ), what is ( f^{-1}(x) )? ( (x + 5)^2 ) ( (x + 5)^{-1} …
1 (Note: None of the given options \((x + 5)^2\), \((x + 5)^{-1}\), \(x - 5\), undefined are correct. The derivative of \(f(x)=x + 5\) is \(1\))
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rendering in a video game engine appears to be slowing down game play. …
\(77\)
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rendering in a video game engine appears to be slowing down game play. …
\(7.5\)
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question 2 if ( f(x)=3 x^{5}-4 x^{2}+3 x + 20 ) find the slope of the t…
\(26\)
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which statement primarily appeals to logos to support the position that…
The first statement: "Although it may come as a surprise, I would prefer a year - round school schedule to our current system. As an academically competitive high school junior, I…
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the function ( f(x) ) is graphed below. how many points on the graph re…
\(2\)
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differentiate ⑤ $\frac{1}{sqrt{x^{3}+1}}$ ⑥ $x^{2}5^{-3x}$
The derivative of \(\frac{1}{\sqrt{x^{3}+1}}\) is \(-\frac{3x^{2}}{2(x^{3}+1)^{\frac{3}{2}}}\)
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determine the domain on which the following function is increasing.
The function is increasing on the domain \((1,\infty)\)
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determine the domain on which the following function is increasing.
The function is increasing on the interval \([0,3]\)
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ii. graph each function by finding the amplitude, period, phase shift, …
Amplitude \( = 2\), Period \(=2\pi\), Phase - shift \(=\text{none}\), Vertical - shift \(=\text{down }3\)
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determine the domain on which the following function is increasing.
The function is increasing on the interval \((-\infty,3)\) (assuming the vertex \(x -\) coordinate is \(3\) from the graph's shape. If we consider the grid - like background (each…
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determine the domain on which the following function is increasing.
The function is increasing on the interval \((1,\infty)\)
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4. (5 points) consider ( f(x)=ln (1 + 3x) ) for ( x ) near 2. a. (3 poi…
a. The local linearization \(L(x)=\frac{3}{7}x+\ln(7)-\frac{6}{7}\) b. The local linearization is an over - estimate. Because \(f^{\prime\prime}(x)=-\frac{9}{(1 + 3x)^{2}}<0\), th…
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determine the domain on which the following function is increasing.
The function is increasing on the interval \((1,\infty)\)
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complete the proof of the identity by choosing the rule that justifies …
The rules for each step (from top - to - bottom) are: Quotient Identity, Pythagorean Identity, Quotient Identity, Simplify (Algebraic simplification), Quotient Identity.
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a spherical balloon is inflated with gas at a rate of 900 cubic centime…
a. When \(r = 20\), \(\frac{dr}{dt}\approx0.18\) \(cm/min\); when \(r = 45\), \(\frac{dr}{dt}\approx0.04\) \(cm/min\). b. The correct option is: If \(\frac{dr}{dt}\) is constant, …
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3. (5 points) let ( f(7)=13 ) and ( f^{prime}(7)=-0.38 ). a. (3 points)…
a. The linear approximation of \(f(7.1)\) is \(12.962\). b. Since \(f^{\prime\prime}(x)>0\) (the function is concave - up), the answer in part (a) is an under - estimate. The tang…
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the radius ( r ) of a sphere is increasing at a rate of 4 inches per mi…
- For \(r = 11\) in: \(6080.24\) \(in^{3}/min\) - For \(r = 34\) in: \(57077.44\) \(in^{3}/min\) - For part (b): If \(\frac{dr}{dt}\) is constant, \(\frac{dV}{dt}\) is proportiona…
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2. (4 points) find the following limit: \\( \\lim _{n \ ightarrow \\inf…
\(\infty\)
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1. (6 points) consider the curve given by the equation: $ln(xy)=2x$. a.…
a. $\frac{dy}{dx}=\frac{y(2x - 1)}{x}$ b. $y = e^{2}x$
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use logarithmic differentiation to evaluate ( f^{prime}(x) ). ( f(x)=(4…
\(f^{\prime}(x)=(4x)^{\ln 4x}\cdot\frac{2\ln(4x)}{x}\)