微積分
極限、導數、最優化與函數性質。
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8. a boy flies a kite which is 120 ft directly above his hand. if the w…
\(18\) ft/min
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6. a 12 foot ladder stands against a vertical wall. the lower end of th…
a. The top of the ladder is moving down at a rate of \(-2\sqrt{3}\text{ ft/sec}\) (the negative sign indicates the downward direction). b. The angle of elevation is changing at a …
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marketing messaging like \limited time offer\ and \act now for the best…
C. Scarcity
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use a system of linear equations to solve the following problem. a new …
B. \(\begin{cases}x + y=18\\2x + 4y=62\end{cases}\)
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5. a spherical hot air balloon is being inflated. air is blown into the…
a. The radius is changing at a rate of \(\frac{1}{18\pi}\approx0.0177\) feet per second. b. The surface area is changing at a rate of \(\frac{4}{3}\approx1.33\) square feet per se…
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4. a rectangular well is 6 feet long, 4 feet wide, and 8 feet deep. if …
The water is rising at a rate of \(\frac{1}{8}\) \(ft/sec\).
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evaluate the function for the given values of x. round to 4 decimal pla…
\(665.1416\)
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question 32, 5.4.37 part 10 of 13 follow the steps for graphing a ratio…
C. The function has no horizontal asymptote. A. The function has one oblique asymptote, \(y=x + 6\)
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graph the logarithmic function f(x) = log(x - 1) + 2.
To graph \(y=\log(x - 1)+2\), first note the vertical asymptote \(x = 1\). Plot the point \((2,2)\) and sketch the curve approaching \(x = 1\) from the right and increasing as \(x…
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(b) suppose that the manager of the food emporium wanted to use the ave…
(b) Using the average rate of change over the interval from 6:00 a.m. to 9:00 a.m. to estimate the number of customers at 7:30 a.m. will under - estimate. Justification: If the fu…
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counting customers in the grocery store he food emporium grocery store …
The average rate of change from 7:30 a.m. to 9:00 a.m. is approximately $103.33$ customers per hour (customers are increasing). The average rate of change from 5:30 p.m. to 9:00 p…
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question consider the graph of the function $f(x)=\\frac{x^{3}-2x^{2}-1…
\(x = 3\)
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the function ( t = f(a) ) models the time, in minutes, for a chemical r…
C. minutes per milliliter per milliliter
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question which of the following are the vertical asymptotes of the grap…
Vertical asymptote at \(x = 2\), Vertical asymptote at \(x = 3\)
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for which of the following does \\( \\lim _ { x \ ightarrow \\infty } f…
E. I and III only
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a particle moves on the hyperbola ( xy = 15 ) for time ( tgeq0 ) second…
A. \(y\) is decreasing by 10 units per second.
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question find the horizontal asymptote for the function given below. gi…
\(y = \frac{7}{3}\)
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a point moves on the x - axis in such a way that its velocity at time t…
C. \(e\)
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for the function ( f ), ( f(x)=2x + 1 ) and ( f(1)=4 ). what is the app…
D. 4.6
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question what is the horizontal asymptote of the graph of ( f(x)=\frac{…
\(y = \frac{4}{5}\)
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follow the steps for graphing a rational function to graph the function…
A. The function has one horizontal asymptote. \(y = \frac{5}{2}\)
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the top of a 15 - foot - long ladder rests against a vertical wall with…
A. \(-\frac{2}{9}\)
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question consider the graph of the function ( f(x)=\frac{x^{3}+7x}{x^{3…
\(-2,7\)
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question find the horizontal asymptote. give your answer in the form ( …
\(y = 0\)
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2. a circle has a radius of 8 inches which is changing. write the follo…
Circumference: \(C = 2\pi r\) Change of Circumference: \(\frac{dC}{dt}=2\pi\frac{dr}{dt}\) Area: \(A=\pi r^{2}\) Change of Area: \(\frac{dA}{dt}=2\pi r\frac{dr}{dt}\)
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2. a circle has a radius of 8 inches which is changing. write the follo…
Circumference: \(C = 2\pi r\) Change of Circumference: \(\frac{dC}{dt}=2\pi\frac{dr}{dt}\) Area: \(A=\pi r^{2}\) Change of Area: \(\frac{dA}{dt}=2\pi r\frac{dr}{dt}\)
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follow the steps for graphing a rational function to graph the function…
For the first part: - Option C: There is no point at which the graph of \(R\) intersects the horizontal or oblique asymptote. For the second part: - The graph of \(R\) is above th…
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follow the steps for graphing a rational function to graph the function…
A. The function has one vertical asymptote, \(x=-2\) A. There is a hole in the graph at the point \((3,\frac{11}{5})\)
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in the triangle shown above, if \\( \\theta \\) increases at a constant…
\(12\) (Option E)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(10500\)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(6000\)
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use finite approximations to estimate the area under the graph of the f…
\(8\)
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find the average rate of change of the function $h(x)=\frac{3}{x + 7}$ …
\(-\frac{1}{40}\)
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41 the uniform crime report gives an accurate account of the actual num…
41. False 42. b. is cruel and unusual punishment 43. a. subculture
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use finite approximations to estimate the area under the graph of the f…
\(0\)
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estimate the area under the graph of ( f(x) = 4x^{3} ) between ( x = 0 …
\(25\)
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estimate the area under the graph of ( f(x)=4x^{3} ) between ( x = 0 ) …
36
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estimate the area under the graph of ( f(x) = 4x^{3} ) between ( x = 0 …
\(9\)
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estimate the area under the graph of ( f(x) = 4x^{3} ) between ( x = 0 …
\(4\)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(1080\)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(378\)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(216\)
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use finite approximation to estimate the area under the graph of ( f(x)…
\(2240\)
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identify the end behavior of the given functions. select the correct an…
For \( m(x)=2^{x}+1\): increases toward positive infinity as \( x\) increases and toward the line \( y = 1\) as \( x\) decreases. For \( n(x)=10^{x - 2}+5\): increases toward posi…
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identify the end behavior of the given functions. select the correct an…
For \(m(x)=2^{x}+1\): increases toward the line \(y = 1\) as \(x\) decreases and increases as \(x\) increases. For \(n(x)=10^{x - 3}+5\): decreases toward the line \(y = 5\) as \(…
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why is language considered an important component of culture? a. it is …
c. It helps people create and transmit culture from one generation to the next by manipulating symbols. True
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use the graph of the rational function to complete the following statem…
\(-\infty\)
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the population of a southern city is growing according to the exponenti…
\(380760\)
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follow the steps for graphing a rational function to graph the function…
C. It approaches \(\infty\) on one side of the asymptote(s) at \(x = 0\) and \(-\infty\) on the other. It approaches \(\infty\) on one side of the asymptote(s) at \(x=-9\) and \(-…
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follow the steps for graphing a rational function to graph the function…
B. The function has two vertical asymptotes. The leftmost asymptote is \(x=-9\), and the rightmost asymptote is \(x = 0\).
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which is the best explanation as to why the islamic golden age was a pe…
Scholars were supported by Islamic leaders and had access to centers of learning.
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chip company produces three products, kin, ike, and bix. each product u…
(a) | Item | Kin | Ike | Bix | |--|--|--|--| | Contribution margin per unit | \(\$68.40\) | \(\$23.66\) | \(\$59.40\) | | Pounds per unit | \(4.5\) | \(2.6\) | \(5.4\) | | Contrib…
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identify the end behavior of the given functions. select the correct an…
For \(m(x)=2^{x}+1\): toward \(+\infty\) as \(x\) increases, toward \(1\) as \(x\) decreases. For \(n(x)=10^{x - 2}+5\): toward \(+\infty\) as \(x\) increases, toward \(5\) as \(x…
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1. (exam 4 review 5b) solve the initial value problem: $g(t)=\\frac{-}{…
\(g(t)=2\ln|t|+3t - 2\)
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problem 1. differentiate the following functions. (a) 4pts. ( f(x)=\fra…
(a) \(f^\prime(x)=\frac{2x\sin(x)+x^{2}\cos(x)+x^{4}\cos(x)}{(1 + x^{2})^{2}}\) (b) \(f^\prime(x)=6\sin(3x)\cos(3x)\sin(4x^{5})+20x^{4}\cos(4x^{5})\sin^{2}(3x)\) (c) \(f^\prime(x)…
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1. (exam 4 review 5b) solve the initial value problem: $g(t)=\\frac{2}{…
\(g(t)=-2\ln|t|-t + 2\)
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3 matching 20 points find the exact value of each trigonometric functio…
\(\tan\theta=-\sqrt{3}\), \(\sin\theta=\frac{\sqrt{3}}{2}\), \(\cos\theta =-\frac{1}{2}\)
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find the exact value of the trigonometric function. \\( \\sin \\theta \…
\(1\)
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follow the steps for graphing a rational function to graph the function…
C. It approaches \(\infty\) on one side of the asymptote(s) at \(x = - 4\) and \(-\infty\) on the other.
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20) $\\int 5 x \\sqrt3{3 x - 1} d x$
\(\frac{5}{21}(3x - 1)^{\frac{7}{3}}+\frac{5}{12}(3x - 1)^{\frac{4}{3}}+C\)
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19) $\\int 2x\\sqrt{3x - 2}dx$
\(\frac{4}{45}(3x - 2)^{\frac{5}{2}}+\frac{8}{27}(3x - 2)^{\frac{3}{2}}+C\)
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18) $\\int (x - 2)^8\\cdot6x dx$
\(\frac{3(x - 2)^{10}}{5}+\frac{4(x - 2)^{9}}{3}+C\)
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the maximum acceleration attained on the interval ( 0 leq t leq 3 ) by …
\(21\) (corresponds to option D)
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find \\( \\sin ( 2 a ) \\), if \\( \\sin ( a ) = - \\frac { 33 } { 65 }…
$\frac{3696}{4225}$
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5. $\\cos ^{2}y-\\sin ^{2}y=1-2\\sin ^{2}y$
The left - hand side \(\cos^{2}y-\sin^{2}y\) is equal to the right - hand side \(1 - 2\sin^{2}y\) after using the Pythagorean identity \(\cos^{2}y+\sin^{2}y = 1\) and simplifying.…
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assignment 9.3: double - angle, half - angle formulas score: 4/13 answe…
$\sin(2x)=\frac{24}{25}$ $\cos(2x)=-\frac{7}{25}$
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select all the correct answers. consider function f and function g. f(x…
The graph of function \(g\) is the graph of function \(f\) reflected over the \(x -\)axis and vertically stretched by a factor of \(5\); Unlike the graph of function \(f\), the gr…
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select the correct answer. which statement about the end behavior of th…
A. As \(x\) decreases, \(y\) approaches the vertical asymptote at \(x =-3\)
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assignment 9.2: sum and difference identities score: 7/8 answered: 7/8 …
$\sin(90^{\circ})$; $1$
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type the correct answer in the box. use numerals instead of words. if n…
\(4\)
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select the correct answer. which statement correctly compares the graph…
B. The graph of function \(g\) is a vertical compression of the graph of function \(f\).
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follow the seven step strategy to graph the following rational function…
A. The equation(s) of the horizontal asymptote(s) is/are \(y = 0\)
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select the correct answer. the maximum occupancy of a concert hall is 1…
B. \(175(1.30)^{t}>1200\)
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use transformations of ( f(x)=\frac{1}{x^{2}} ) to graph ( g(x)=\frac{1…
First, shift the graph of \(y = \frac{1}{x^{2}}\) \(3\) units to the left to obtain the graph of \(y=\frac{1}{(x + 3)^{2}}\). Then, shift the graph of \(y=\frac{1}{(x + 3)^{2}}\) …
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use the graph of the rational function to complete the following statem…
\(\infty\)
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use the graph of the rational function to complete the following statem…
\(\infty\)
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what was the impact of cities such as baghdad and cordoba on trade and …
They spread knowledge, scientific advancements, and cultural practices that influenced other regions and civilizations.
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how did the spread of islam impact education in west african kingdoms? …
It led to the establishment of Islamic schools where subjects like math, science, and literature were taught.
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show me how to graph f(x)=x^3 - 2x^2
Follow the above steps to graph the function \(y = x^{3}-2x^{2}\).
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show me how to graph f (x) = x3 - 4x2
To graph \(y = x^{3}-4x^{2}\): - Mark the intercepts \((0,0)\) and \((4,0)\). - Use the first - derivative information to identify where the function is increasing (\((-\infty,0)\…
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assignment 9.2: sum and difference ide score: 3/8 answered: 3/8 questio…
\(2-\sqrt{3}\)
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assignment 9.2: sum and differenc score: 2/8 answered: 2/8 question 3 c…
\(\frac{\sqrt{2}-\sqrt{6}}{4}\)
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a particle moves on the hyperbola ( xy = 15 ) for time ( tgeq0 ) second…
C. \(y\) is decreasing by 5 units per second.
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assignment 9.2: sum and difference identities score: 0/8 answered: 0/8 …
\(-\frac{\sqrt{2}+\sqrt{6}}{4}\)
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assignment 9.1: trigonometric identities score: 17/20 answered: 13/16 q…
\(\sec(t)\)
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which is an advantage of using modern currency instead of a barter syst…
C. ability to store and use a form that is accepted everywhere
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review the water quality report and then answer the question. springfie…
to inform residents about the source and content of Springfield's drinking water
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review the water quality report and then answer the question. springfie…
The writer defines unfamiliar terms (ppm) and informs readers that the water is safe.
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read the water quality report and then answer the question. springfield…
residents of Springfield
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follow the steps for graphing a rational function to graph the function…
C. There is no oblique asymptote. A. The graph of \(R\) intersects the horizontal or oblique asymptote at \((0,0)\)
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in what ways did trade routes contribute to the cultural richness of af…
By facilitating the exchange of goods, ideas, and cultural practices
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how did the spread of islam impact education in west africa? it led to …
It led to the establishment of schools and universities where subjects like math, science, and literature were taught.
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how did the emphasis on education and learning impact african societies…
It led to increased literacy rates and a high value placed on knowledge and innovation.
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how did the emphasis on education and learning impact african societies…
It led to increased literacy rates and a high value placed on knowledge and innovation.
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how did the spread of islam impact education in west africa? it limited…
It led to the establishment of schools and universities where subjects like math, science, and literature were taught.
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what was one effect of the introduction of arabic numerals and mathemat…
It improved trade and recordkeeping, making economic activities more efficient.
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follow the steps for graphing a rational function to graph the function…
A. It approaches \(\infty\) on one side of the asymptote(s) at \(x=-2\) and \(-\infty\) on the other. It approaches either \(\infty\) or \(-\infty\) on both sides of the asymptote…
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a point moves on the x - axis in such a way that its velocity at time t…
C. \(e\)
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how did the development of improved irrigation methods benefit african …
It provided more food, helping societies thrive.
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assignment 9.1: trigonometric identities score: 4/20 answered: 4/16 que…
\(\cos^{2}(t)\)