微積分
極限、導數、最優化與函數性質。
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find the derivative. $\frac{d}{dt}4(t^{2}+5t)^{-6}$ $\frac{d}{dt}4(t^{2…
$-\frac{24(2t + 5)}{(t^{2}+5t)^{7}}$
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find the derivative of the function. y = - 9(9x^{2}+5)^{-6} \\frac{dy}{…
$\frac{972x}{(9x^{2}+5)^{7}}$
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complete each sentence with the correct piece of environmental legislat…
The Endangered Species Act obligates federal and state governments to protect all species threatened with extinction. The Clean Air Act limits air pollution from industries and ca…
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find the derivative. $\frac{dy}{dx}$ if $y(x)=sqrt{x^{2}+1}$ $\frac{dy}…
$\frac{x}{\sqrt{x^{2}+1}}$
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the storyteller by saki. it was a hot afternoon, and the railway carria…
None of the provided options are correct as the bachelor's story in "The Storyteller" is more about subverting traditional moral lessons rather than supporting any of these themes.
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find g(x) if g(x) = 6xe^{8x}. g(x)=□
$6e^{8x}(1 + 8x)$
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find f(x) and find the equation of the line tangent to the graph of f a…
$f'(x)=4xe^{x^{2}}-5$; The equation of the tangent line at $x = 0$ is $y=-5x + 10$; There are no real values of $x$ for which the tangent line is horizontal.
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19. recent studies seem to indicate the population of north american po…
(a) 11 years (b) Graph as described above (c) Maximum: 1200, Minimum: 700
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how does the characterization of cyril contribute to the satire in \the…
through his refusal to do what he is told
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when planning a career, which of the following is important to identify…
the skills that one already has
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3. what were the portuguese explorers bringing back to europe, and from…
3. Spices, gold, and luxury goods from India and Africa. 4. Spain. 5. Europe's peninsulas, harbors, and proximity to other continents facilitated sea exploration.
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14. max: 12,000, min: 6500, p = 10. use the information given to write …
For the temperature in Geneva: Sinusoidal equation $T(t)=5\cos(\frac{\pi}{12}t)+34$, times when $T = 32$ are $t=\frac{12}{\pi}\cos^{-1}(-\frac{2}{5})$ and $t=\frac{12}{\pi}(2\pi-\…
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there was a wave of reaction in favour of the story; the word horrible …
None of the provided options are correct. The under - lined sentence shows that the aunt's culturally influenced tales lack the 'ring of truth' that the new story has, indicating …
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12. find the maximum and the minimum values of the function subject to …
(a) Maximum: \(1\), Minimum: \(\sqrt[3]{2}\) (b) Maximum: \(100\), Minimum: \(-100\) (c) Maximum: \(9\), Minimum: \(-9\) (d) Maximum: \(3\sqrt{3}\), Minimum: \(-3\sqrt{3}\)
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formal test you are driving on a dry road, and it begins to rain. you s…
Slow down and plan for at least two times the normal stopping distance.
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11. find the shortest distance from the point (0, 0, 8) to the plane x …
The shortest distance is $\frac{9\sqrt{14}}{7}$ for all three methods.
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formal test at night, if you leave a brightly lit place, you should dri…
Drive slowly until your eyes adjust to the darkness
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10. find the dimensions of the cardboard box (shaped like a rectangular…
The dimensions of the box are length $l = 4$ feet, width $w = 4$ feet and height $h = 2$ feet.
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9. show that $f(x,y)=y^{2}+y^{4}$ has infinitely many critical points (…
We have shown that $f(x,y)=y^{2}+y^{4}$ has infinitely many critical points of the form $(x,0)$ for all real $x$, the second - derivative test is inconclusive for these points, an…
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the ability to earn money in exchange for work provided is known as \ea…
One can get additional education or training to qualify for a higher - paying job, such as a high - school graduate pursuing a nursing degree to earn a higher salary.
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given the function $f(x)=-x^{2}+5x + 14$, determine the average rate of…
$-4$
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the function y = f(x) is graphed below. what is the average rate of cha…
$-8$
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the function y = f(x) is graphed below. what is the average rate of cha…
25
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the function y = f(x) is graphed below. what is the average rate of cha…
20
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the function y = f(x) is graphed below. what is the average rate of cha…
$-\frac{3}{5}$
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the function y = f(x) is graphed below. what is the average rate of cha…
$\frac{1}{5}$
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the function y = f(x) is graphed below. what is the average rate of cha…
$-1.4$
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the function $y = f(x)$ is graphed below. what is the average rate of c…
$10$
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the function y = f(x) is graphed below. what is the average rate of cha…
$-1.6$
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how did populists want the government to handle currency in the late 18…
Populists wanted the government to make unlimited silver coins.
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8. for the following functions find all of the critical points and then…
### (a) Critical points: $(0,0)$ (saddle point), $(\frac{1}{3},\frac{1}{6})$ (local minimum) ### (b) Critical points: $(0,0)$ (saddle point), $(2,2)$ (local minimum) ### (c) Criti…
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8. for the following functions find all of the critical points and then…
The process to find critical points and classify them for a function $z = f(x,y)$ involves finding first - order partial derivatives to get critical points, then second - order pa…
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what was the purpose of gothic architecture in medieval cathedrals? to …
To inspire wonder with their large and impressive design.
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section 3.4 the chain question 16, 3.4.51 find the derivative. f(x) if …
$12x^{3}e^{x^{4}}(e^{x^{4}} + 1)^{2}$
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8. for the following functions find all of the critical points and then…
For $f(x,y)=x^{3}-2xy + 8y^{3}$, the critical points are $(0,0)$ (saddle point) and $(\frac{1}{3},\frac{1}{6})$ (local minimum). The process for other functions is similar as show…
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find the derivative of the following function. y = \\frac{-5}{(3x^{3}+5…
$\frac{90x^{2}}{(3x^{3}+5)^{3}}$
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find f(x) and find the value(s) of x where the tangent line is horizont…
\(f^\prime(x)=12x^{4}(x - 12)^{6}(x - 5)\); The values of \(x\) where the tangent line is horizontal are \(x = 0\), \(x = 5\), and \(x = 12\).
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find f(x) and find the value(s) of x where the tangent line is horizont…
\(f'(x)=8x^{2}(x - 8)^{4}(x - 3)\); The values of \(x\) where the tangent line is horizontal are \(x = 0\), \(x = 3\), and \(x = 8\).
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find f(x) and find the value(s) of x where the tangent line is horizont…
$f'(x)=\frac{-12x - 5}{(6x - 5)^{4}}$; $x = -\frac{5}{12}$
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find f(x) and find the value(s) of x where the tangent line is horizont…
$f^\prime(x)=\frac{x - 7}{\sqrt{x^{2}-14x + 51}}$; $x = 7$
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7. does $f(x,y):=sqrt{x^{2}+y^{2}}$ have any critical points? where is …
The critical point is $(0,0)$ and the absolute minimum value of the function $f(x,y)$ in the region $x^{2}+y^{2}\leq10$ is $0$ at the point $(0,0)$.
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find the derivative. $\frac{d}{dx}3x(x^{6}+1)^{8}$ $\frac{d}{dx}3x(x^{6…
\(3(x^{6}+1)^{7}(49x^{6}+1)\)
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consider this claim. the federal government should protect national par…
Staff at Yosemite National Park report that an increase in visitors has led to problems such as smog and trail erosion.
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find the derivative. \\(\\frac{d}{dt}\\frac{(3t - 4)^3}{t + 5}\\) \\(\\…
$\frac{(3t - 4)^{2}(6t + 49)}{(t + 5)^{2}}$
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journeys to america early asian immigration early immigration and the g…
The company was able to pay Chinese immigrants lower wages.
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the theme of \the tide rises, the tide falls\ is best stated as - * hum…
the ocean goes on, but human life is limited
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answer the following questions to review the presidency of bill clinton…
tariffs
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question 9 1 pts an author writing for a modern teen audience includes …
The allusion may become dated and meaningless to future readers, limiting the text's longevity
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a research group using hospital records developed an approximate mathem…
$1.09$
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find f(x) and find the equation of the line tangent to the graph of f a…
$f^{\prime}(x)=\frac{2}{\sqrt{4x - 7}}$; Tangent line: $y=\frac{2}{3}x+\frac{1}{3}$; No values of $x$ for horizontal tangent.
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find f(x) and find the equation of the line tangent to the graph of f a…
$f^{\prime}(x)=\frac{2}{\sqrt{4x - 7}}$; Equation of tangent line: $y=\frac{2}{3}x+\frac{1}{3}$; No values of $x$ for horizontal tangent line.
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find the derivative. f(x)=4\\sqrt{6x^{2}+7} f(x)=□
$\frac{24x}{\sqrt{6x^{2}+7}}$
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find f(x). f(x)=e^{7x} f(x)=□
$7e^{7x}$
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2) (g(u)=3^{4u - 1}): find (g(t))
$g^{\prime}(t)=4\cdot3^{4t - 1}\ln 3$
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work: section 3.4 the chain question 5, 3.4.21 find f(x). f(x)=(3x^6 + …
$90x^{5}(3x^{6}+1)^{4}$
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replace ? with an expression that will make the equation valid. $\frac{…
$-8x$
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replace ? with an expression that will make the equation valid. $\frac{…
$2$
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6. the tell - tale heart is a ______. a. novel b. play c. short story d…
1. D. I'm excited for the party tonight 2. C. short story 3. B. Edgar Allan Poe 4. D. vulture's 5. B. Pitch - black 6. D. dramatic irony
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differentiate the following function. f(x)=9 - 2x + 3e^x f(x)=□
$-2 + 3e^x$
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use a graph or a table to find the following limit. lim(x→∞) log₈(x) li…
$\infty$
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find f(x). f(x)= - 7\\ln x + 5x^{2}-7 f(x)=\\square
$-\frac{7}{x}+10x$
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find the derivative of f with respect to x of f(x) = ln x^2. the deriva…
$\frac{2}{x}$
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use a graph or a table to find the following limit. lim log₄(x) x→0⁺ li…
$-\infty$
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find f(x). f(x) = ln x^{10}+5 ln x f(x) =
$\frac{15}{x}$
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section 3.2 derivatives, exponential and logarithmic question 10, 3.2.5…
$\frac{3}{x}+\frac{8}{x\ln 3}$
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find $\frac{dy}{dx}$ for the indicated function y. y = 12^x+e^3 $\frac{…
$12^x\ln(12)$
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find the equation of the line tangent to the graph of f at the indicate…
$y=-x + 2$
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a student claims that the line tangent to the graph of f(x)=e^x at x = …
Is the student correct in saying that the line tangent to the graph of $f(x)=e^{x}$ at $x = 1$ passes through the point $(0,0)$? - B. Yes Will the line tangent at $x = 2$ pass thr…
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first use the appropriate properties of logarithms to rewrite f(x), and…
Rewrite $f(x)$: $20x+\ln20+\ln x$ $f^{\prime}(x)$: $20+\frac{1}{x}$
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first use appropriate properties of logarithms to rewrite f(x), and the…
$-\frac{1}{x}$
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find $\frac{dy}{dx}$ $y = 7ln x+8log_7x$ $\frac{dy}{dx}=square$ (type a…
$\frac{7}{x}+\frac{8}{x\ln 7}$
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find $\frac{dy}{dx}$ for the indicated function y. y = 10^x + e^2 $\fra…
$10^x\ln 10$
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an investment of $10,000 earns interest at an annual rate of 8% compoun…
$938.81$
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the total sales of s (in thousands of dvds) of a certain movie are give…
21120
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the total sales of s (in thousands of dvds) of a certain movie are give…
B. After 5 months, the total sales are 16,000 DVD's and the sales are increasing at the rate of 5.12 DVD's per month.
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the total sales of s (in thousands of dvds) of a certain movie are give…
$5.12$
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the total sales of s (in thousands of dvds) of a certain movie are give…
$16.00$
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the total sales of s (in thousands of dvds) of a certain movie are give…
$\frac{16000t}{(t^{2}+100)^{2}}$
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differentiate the function. y=(x + 6)(x^3+2x + 1) y=
$4x^{3}+18x^{2}+4x + 13$
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find the indicated derivative and simplify. $\frac{d}{dx}2xlog x^{6}$ $…
$12\log x+\frac{12}{\ln 10}$
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find $\frac{dy}{dt}$. $y=(30 + e^{t})ln t$ $\frac{dy}{dt}=square$ (type…
$\frac{30 + e^{t}}{t}+e^{t}\ln t$
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find the indicated derivative and simplify. y for y = (8 + 7x - 9x^2)e^…
$e^{x}(-9x^{2}-11x + 15)$
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find the indicated derivative and simplify. y for y = $\frac{5x - 3}{x^…
$\frac{-5x^{2}+6x + 24}{(x^{2}+8x)^{2}}$
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use the product rule to find the derivative. y=(5x^2 + 2)(4x - 5) y=
$60x^{2}-50x + 8$
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find f(x). f(x)=\frac{ln x}{14 + x} f(x)=square (type an exact answer.)
$\frac{14 + x - x\ln x}{x(14 + x)^{2}}$
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find f(x). f(x)=\frac{8 - e^{x}}{7 + e^{x}} f(x)=square
$\frac{-15e^{x}}{(7 + e^{x})^{2}}$
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find f(x). f(x)=(0.3x + 9)(0.2x - 2) f(x)=□
$0.12x + 1.2$
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read the passage and dictionary entry. hannah is researching the civil …
B. function
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use the product rule to find the derivative. y=(5x^2 + 3)(2x - 5) y=□
$30x^{2}-50x + 6$
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find f(x). f(x)=3x^{5}ln x f(x)=□
$3x^{4}(5\ln x + 1)$
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find f(x). f(x)=4xe^x f(x)=□
$4e^{x}(1 + x)$
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find f(x). f(x)=\frac{4x - 7}{9x + 1} f(x)=square
$\frac{67}{(9x + 1)^2}$
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starting with a 140 - foot - long stone wall, a farmer would like to co…
\(x = 210\), \(w = 175\)
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find f(x) and simplify. f(x) = \\frac{x}{x + 50} which of the following…
A. $\frac{(x + 50)(1)-(x)(1)}{(x + 50)^{2}}$ $f^\prime(x)=\frac{50}{(x + 50)^{2}}$
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find f(x) and simplify. f(x)=\frac{x}{x + 50} which of the following sh…
A. $\frac{(x + 50)(1)-(x)(1)}{(x + 50)^2}$
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section 3.3 derivatives and quotients question 4, 3.3.12 find f(x). f(x…
$36x + 39$
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find f(x) and simplify. f(x)=8x^5(x^4 - 9) which of the following shows…
$72x^{8}-360x^{4}$
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which of the following describes creative work that can be used without…
B. Public domain
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f(x)=8x^{5}(x^{4}-9) which of the following shows the correct applicati…
C. $(8x^{5})(4x^{3})+(x^{4}-9)(40x^{4})$
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find (a) the derivative of $\frac{t(x)}{b(x)}$ without using the quotie…
$5x^{4}$