微積分
極限、導関数、最適化、関数挙動。
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let $f(x)$ be a function defined as follows: $f(x) = \\begin{cases} x^2…
R only
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what does \scarce resources\ mean? there are no resources available. th…
There is a limit on the availability of resources.
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calculate the following limit: \\(\\lim\\limits_{x\\to 9} \\dfrac{9 - x…
6
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calculate the following limit: \\(\\lim\\limits_{x\\to 2} \\dfrac{5}{(x…
Does Not Exist
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which of the following is best described as the study of allocating sca…
economics
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which of the following is false? a) every continuous function is differ…
A. Every continuous function is differentiable.
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question 6 calculate \\(\\lim\\limits_{x\\to -1} \\dfrac{4\\left(x^2 - …
0
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for which value of k will the following piecewise function be continuou…
A. 0
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graph $y = 9x$.
# Explanation: ## Step1: Identify the slope-intercept form The equation \( y = 9x \) is in the slope - intercept form \( y=mx + b \), where \( m \) is the slope and \( b \) is the…
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5 the slope of the graph given below is note: simplify your answer and …
-2
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for questions 16 - 19, use the functions ( f(x)=dots ) to find each fun…
$-55$
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4 look at the graph shown below. find the slope. a 3 b $-\frac{3}{4}$ c…
B. $-\frac{3}{4}$
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3 the slope of the graph shown below is: a \\(\\frac{5}{4}\\) b \\(-\\f…
B. $-\frac{5}{4}$
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2 examine the following graph: find the slope. simplify the answer and …
9/14
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does $f(x) = \\frac{x^2 - 36}{x - 5}$ have a discontinuity? if so, what…
C. \( f(x) \) has an infinite discontinuity at \( x = 5 \). ### Second Question (Average Velocity of \( s(t)=3t^{2}+6t \) over \([1,1 + h]\))
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1 what is the slope of the line? a 1/2 b 2 c -1/2 d -2
C) -1/2
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graph $y = -5x$.
# Explanation: ## Step1: Identify the slope - intercept form The equation of a line in slope - intercept form is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.…
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question 1 let $f(x) = \\frac{x - 4}{\\sqrt{x + 3}}$ what is the domain…
$\boldsymbol{(-3,\infty)}$ (corresponding to the option: $(-3,\infty)$)
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x 0 3 y = \\frac{1}{3}x + 2 2 \\square plot the ordered pairs and draw …
3
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fill in the blank question dating from the mid - 1800s, a series of agr…
unequal
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precision complete the table. x 0 1 y = 3x - 1 -1 3 plot the ordered pa…
Corrected table: | \( x \) | 0 | 1 | | --- | --- | --- | | \( y = 3x - 1 \) | -1 | 2 | Ordered pairs: \( (0, -1) \) and \( (1, 2) \). Graph is a line through these points with slo…
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find the sum. 244 + _____ = 327 _____ + 143 = 281
For the first equation, the number is \(83\); for the second equation, the number is \(138\)
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find the most general antiderivative or indefinite integral. \\(\\int 1…
\(\frac{10}{\sqrt{5}+1}x^{\sqrt{5}+1}+C\) (or \(\frac{5(\sqrt{5}-1)}{2}x^{\sqrt{5}+1}+C\) after rationalizing the denominator)
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the graph of a rational function ( y = f(x) ) is given. use the graph t…
C. The solution set is the empty set.
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express the function graphed on the axes below as a piecewise function.…
$$ f(x) = \begin{cases} -\dfrac{5}{4}x - \dfrac{9}{2} & \text{for } x < -2 \\ x - 5 & \text{for } x > 0 \end{cases} $$
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the graph of a rational function y = f(x) is given. use the graph to gi…
C. The solution set is the empty set.
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evaluating functions, a graph - notes use the graph for 14 - 17. 14. fi…
\( f(0) = 0 \) ### Question 15: Find \( f(-4) \)
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equations, inequalities, model question 1, 5.3.1 part 2 of 3 hw score: …
To solve the problem, we analyze the graph of the rational function \( y = f(x) \): ### Part (a): Solution set of \( f(x) = 0 \) The solution to \( f(x) = 0 \) occurs where the gr…
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find the slope of the line passing through the points (-7, -4) and (0, …
$\frac{4}{5}$
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Question was provided via image upload.
B. The solution set is the empty set, \( \varnothing \).
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find the slope of the line passing through the points (-4, 3) and (-7, …
$-1$
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f) $y_1 = \\frac{2x}{3} + \\frac{1}{2}$ $y_2 = \\frac{3x}{2} - \\frac{1…
| $x$ | $-3$ | $-2$ | $-1$ | $0$ | $1$ | $2$ | |-----|------|------|------|-----|-----|-----| | $y_1$ | $-1.5$ | $-0.83$ | $-0.17$ | $0.5$ | $1.17$ | $1.83$ | | $y_2$ | $-4.83$ | …
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a line that includes the points (0, -10) and (9, d) has a slope of \\(\…
$d=-2$
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question use technology to find points and then graph the function ( y …
Some points on the graph are \((0,0)\), \((2,2)\), \((4,4)\), \((6,2)\), \((8,0)\). The graph is an inverted V - shaped graph with vertex at \((4,4)\) passing through the above - …
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question use synthetic division to find the result when $2x^4 - 15x^3 +…
$2x^3 - 7x^2 - x - 2$ (with a remainder of $0$)
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solve this system of equations by graphing. first graph the equations, …
The solution to the system is $(-2, -1)$
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divide. 4.4÷2.2 4.4÷2.2 = \\square (type a whole number or a decimal.)
2
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in 2–3 sentences, answer: why is it risky to rely too heavily on only o…
Relying too heavily on one source is risky because it may offer a limited, one - sided perspective, lack sufficient evidence or counter - arguments, and ultimately reduce the essa…
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(\frac{1}{2} \times 4\frac{3}{4} = square) (simplify your answer. type …
$2\frac{3}{8}$ or $\frac{19}{8}$
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n operation (+, −, ×, ÷), an exponent, or a fraction bar t n below. go …
47
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draw an area model to show $\frac{1}{2} \times 4\frac{3}{4}$. find the …
C. <The area model showing half of 4 and 3/4 units, equivalent to 2 and 3/8 units>
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if $g(x) = x^2$ and $f(x) = x + 3$ calculate $f(g(x))$ 1. identify the …
\( 8x - 1 \) ### Problem 2:
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solve. \\( 1\\frac{3}{7} \\div \\frac{1}{2} = \\frac{\\square}{\\square…
$\frac{3}{7} \div \frac{1}{2} = \frac{3}{7} \times \frac{2}{1} = \frac{6}{7}$
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find the coordinates for the vertex of the following quadratic function.
\((6, -4)\)
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click on an operation (+, −, ×, ÷), an exponent, or a fraction bar to s…
88
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6 - (2³ - 8)/2 6 - (8 - 8)/2 6 - 0/2
6
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y = -3x + 3; 6x + 2y = 6; solution: handwritten steps; graph grid
The system has infinitely many solutions, and the graph is the line $y=-3x+3$ passing through $(0,3)$ and $(1,0)$.
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graph the system below and write its solution.\\begin{cases}6x + 2y = -…
No solution
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Question was provided via image upload.
Yes, \( x = 0 \) makes the function undefined (division by zero is not allowed). ### Final Answers (Key Parts) - Machine A Outputs: \( 10, -6 \) - Machine B Outputs: \( 26, 10 \) …
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give an example of how the government can limit your rights.
One example is during a pandemic, the government may impose stay - at - home orders to limit the right to freedom of movement in order to control the spread of the disease and pro…
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find the parabola with equation $y = ax^2 + bx$ whose tangent line at $…
\(y = 3x^{2}-2x\)
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find an equation of the tangent line to the curve ( y = xsqrt{x} ) that…
\( y = 9x-108 \)
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14. 75,303 - ______ = 74,464 15. 83,300 - ______ = 75,565 16. 33,883 - …
839 ### Question 15
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determine the domain on which the following function is increasing.
The function is increasing on the domain $(2, \infty)$
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determine the domain on which the following function is decreasing.
$(-\infty, -4)$
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read the statement below: \free speech should be limited when it causes…
Free speech should be limited when it causes harm requires careful reasoning because defining “harm” is subjective (e.g., distinguishing hate speech from legitimate dissent) and b…
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analyzing the graph of a quadratic function the function ( f(x) = -0.3(…
- The axis of symmetry is $x = 5$. - The domain is $\{x| x \text{ is a real number}\}$. - The function is increasing over $(-\infty, 5)$.
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when we take antiderivatives. it is look at the integrand and think abo…
\(\boxed{\frac{1}{2} \sin^{-1}(2x) + C}\)
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transform the solid black function to match the dotted function. ( y = …
$-f(x+0)+0$ or simplified as $-x^2$
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graph ( h(x) = 0.5(x + 2)^2 - 4 ) by following these steps: step 1: ide…
$h(-4) = -2$, $h(-6) = 4$ To complete the graph, plot the points $(-4, -2)$ and $(-6, 4)$, then reflect them across the axis of symmetry $x=-2$ to get $(-0, -2)$ and $(2, 4)$, the…
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missing minuend and subtrahend problems grade 6 subtraction worksheet f…
\( 839 \) ### Problem 15:
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have something similar when wook at the integrand and think n rule, the…
\( \frac{(x^3 + 4)^6}{3}+C \)
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write an equation for each graph 3. 4.
To solve for the equations of the polynomial graphs, we use the fact that if a graph has a root at \( x = a \), then \( (x - a) \) is a factor. The multiplicity of the root (even …
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12. graph: $y = \\frac{3}{4}x$ 14. solve: $\\frac{e}{5} = \\frac{5}{6}$
s: - For problem 12: The graph is a straight line passing through \((0,0)\), \((4,3)\), \((-4,-3)\) etc. (plotted on the given grid). - For problem 14: \( e=\frac{25}{6} \) (or \(…
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3.1 periodic phenomena ap precalculus 3.1 practice the following graphs…
To solve these problems, we analyze the periodic function's behavior using the given one - period graph and the properties of periodic functions (periodic functions repeat their b…
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5) $(-6.2)+(-6.9)$ a) $-5.7$ b) $-13.1$ c) $-9.6$ d) $-7.1$ 6) $(-4.3)-…
B) -13.1 ### Problem 6: $(-4.3)-(-5.7)$
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lesson 2: absolute value & operations with integers directions: solve e…
1. $8$ 2. $10$ 3. $-7$ 4. $10$ 5. $11$ 6. False 7. True 8. $-7, -5, 4$ 9. $-110$ (Note: For the drawing components: 1. Draw the hair for answer 8 2. Draw the nose for answer 10 3.…
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type the correct answer in the box. use numbers instead of words. enter…
-4.25
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type the correct answer in the box. use numbers instead of words. an ex…
-13.28
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directions: solve each problem, showing all work. then find the answer …
1. $-5$ (color purple) 2. $21$ (color yellow) 3. $60$ (color orange) 4. $12$ (color pink) 5. $-12$ (color light green) 6. $31$ (color light blue) 7. $-16$ (color dark blue) 8. $-4…
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sol review: square roots, real numbers, and interest 4028090@ccpsnet.ne…
-10 (corresponding to the option: -10)
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compute. -3.384 - 5.76 = 14.25 + (-27.381) =
$-3.384 - 5.76 = -9.144$ $14.25 + (-27.381) = -13.131$
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compute. -3.384 - 5.76 = 14.25 + (-27.381) =
$-3.384 - 5.76 = -9.144$ $14.25 + (-27.381) = -13.131$
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type the correct answer in the box. use numbers instead of words. what …
-19.527
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an expression is shown. $-\frac{1}{5} + 0.15$ which value is equivalent…
D. $-\frac{1}{20}$
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compute. -2.34 + (-6.52) = -2.8 + 45.3 =
$-2.34 + (-6.52) = -8.86$ $-2.8 + 45.3 = 42.5$
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consider the polynomial function $q(x) = 3x^4 - 5x^3 - 2x^2 + x - 18$. …
As $x$ approaches positive infinity ($x\to\infty$), $q(x)$ approaches positive infinity ($q(x)\to\infty$); as $x$ approaches negative infinity ($x\to-\infty$), $q(x)$ approaches p…
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compute. -2.34 + (-6.52) = -2.8 + 45.3 =
$-2.34 \div (-6.52) \approx 0.36$ $-2.8 \div 45.3 \approx -0.06$
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consider the polynomial function $h(x) = -7x^6 + 3x^4 - 5x^2$. what is …
As $x$ approaches positive infinity, $h(x)$ approaches negative infinity; as $x$ approaches negative infinity, $h(x)$ approaches negative infinity. Or concisely: $\text{As } x\to\…
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consider the polynomial function $h(x) = -2x^5 + 8x^4 - 2x^2 + 15$. wha…
As $x \to +\infty$, $h(x) \to -\infty$; as $x \to -\infty$, $h(x) \to +\infty$
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how can place value help me add 316 and 482? find 316 + 482. 316 = 300 …
1. For the fill-in: break apart 2. $316 + 482 = 798$ 3. Place value helps by letting you break numbers into hundreds, tens, and ones, add each place value group separately, then c…
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316 = 300 + 10 + 6 +482 = 400 + 80 + 2 700 + 90 + 8 316 + 482 = \\boxed…
798
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what is 9,000 + 600 + 70 + 11?
9681
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recall your knowledge from previous lessons. use words to describe the …
The graph of \( f(x)=(x - 1)^2 \) is the graph of \( f(x)=x^2 \) shifted 1 unit to the right. ### 2. For \( f(x) = (x + 1)^2 \)
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the figure above is the graph of the function m(t). let n(t) = m(t) + 2…
1. $n(-3)=1$ 2. $n(2)=8$ 3. $k(2.5)=6$ 4. $w(1.5)=5.5$ 5. $w(-1.5)=-0.5$ 6. $p(2)=8$
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7. for each function, state the locator point (h,k), then sketch the gr…
a. Locator point: $(-1, -3)$ b. Locator point: $(3, 4)$ c. Locator point: $(0, -3)$ --- ### Problem 8
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what is 521 + 314? find the sum. first, break apart 521 into hundreds, …
First, the breakdown of 521 is: $521 = 500 + 20 + 1$ The final sum of $521 + 314$ is $835$
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multiply these fractions. cancel and simplify if necessary. 1. $1\\frac…
\(2\frac{5}{8}\) ### Problem 2: \(2\frac{1}{3} \times 5\frac{2}{5}\)
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mplete the following tables with values for the functions ( f ), ( g ) …
| $x=$ | -3 | -2 | -1 | 0 | 1 | |------|----|----|----|---|---| | $f(x)=$ | $-f(3)$ | $-f(2)$ | $-2$ | $0$ | $2$ | | $g(x)=$ | $g(3)$ | $g(2)$ | $2$ | $0$ | $2$ | | $h(x)=$ | $h(3…
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if $f(x) = x^2 + 3$, find and simplify the following: (a) $f(t + 8) =$ …
(a) $t^2+16t+67$ (b) $t^6+16t^3+67$ (c) $12$ (d) $3t^2+9$ (e) $t^4+6t^2+17$
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polynomial functions and end behavior practice describe the end behavio…
1. $\lim_{x\to-\infty} g(x) = -\infty$, $\lim_{x\to\infty} g(x) = \infty$ 2. $\lim_{x\to-\infty} p(x) = \infty$, $\lim_{x\to\infty} p(x) = \infty$ 3. $\lim_{x\to-\infty} f(x) = \i…
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solve the equation using the substitution $(x - y)dx + xdy = 0$ $xdy = …
The general solution of the differential equation \((x - y)dx + xdy = 0\) is \(y = Cx-x\ln|x|\) (where \(C\) is an arbitrary constant).
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5. $f(x) = x^3 + 4x^2 - 3$ $limlimits_{x \\to -\\infty} f(x) = -\\infty…
$\lim_{x\to-\infty} f(x) = -\infty$ $\lim_{x\to\infty} f(x) = \infty$
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nction using limit notation. 2. $p(x) = 7x^4 + 3x^3 - 3x - 4$ $limlimit…
For $p(x)=7x^4+3x^3-3x-4$: $\lim_{x\to\infty} p(x) = \infty$ $\lim_{x\to-\infty} p(x) = \infty$ For $f(x)=x^3+4x^2-3$: $\lim_{x\to\infty} f(x) = \infty$ $\lim_{x\to-\infty} f(x) =…
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a laptop computer was purchased for $1600. each year since, the resale …
$y = 1600(0.73)^t$
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identify the graph of the function; y = -\\frac{2}{3}x + 5
The correct graph is the second one (top row, right of the checked incorrect graph): a line with a gentle downward slope crossing the y-axis at 5.
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5. $f(x) = x^3 + 4x^2 - 3$ $limlimits_{x \\to -\\infty} f(x) = \\infty$…
$\lim_{x\to-\infty} f(x) = -\infty$ $\lim_{x\to\infty} f(x) = \infty$
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5. which statement correctly completes the comparison below? the produc…
A. 10 times more
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use the interactive graph below to sketch a graph of $y = 3\\log_2(-x) …
1. Vertical Asymptote: $x=0$ (the y-axis) 2. Key points to plot: $(-1, -9)$, $(-2, -6)$ (or $(-4, -3)$) 3. The graph is a reflected (over y-axis), vertically stretched (by factor …
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consider the exponential function g where $g(x) = 6(3.2)^x$. what is th…
$y = 0$