Cálculo
Límites, derivadas, optimización y comportamiento de funciones.
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which of the following types of data allows researchers to gather infor…
C. quantitative
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step 2 to find $\frac{dy}{dx}=y$ for $x^{3}+y^{8}=6$, we differentiate …
$8y^{7}y'=-3x^{2}$; $y'=-\frac{3x^{2}}{8y^{7}}$
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step 1 when finding $\frac{dy}{dx}=y$ by implicit differentiation, we c…
$\frac{d}{dx}[6]=0$, $\frac{d}{dx}[x^3]=3x^{2}$
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5. how were workers treated during the gilded age?
Workers during the Gilded Age generally faced long working hours, low wages, dangerous work environments, and had limited job security. There was also significant opposition to un…
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when finding $\frac{dy}{dx}=y$ by implicit differentiation, we consider…
\(8y^{7}\)
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2. let (f(x)=|x - 2|). (a) use the definition of derivative to determin…
(a) $f^{\prime}(2)$ does not exist because $\lim_{h ightarrow0^{-}}\frac{f(2 + h)-f(2)}{h}=-1$ and $\lim_{h ightarrow0^{+}}\frac{f(2 + h)-f(2)}{h}=1$ and the left - hand and right…
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find $\frac{dy}{dt}$. $y = 2t(3t^{3}-4)^{4}$ $\frac{dy}{dt}=square$
$2(3t^{3}-4)^{3}(39t^{3}-4)$
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use implicit differentiation to find an equation of the tangent line to…
$y=x+\frac{1}{4}$
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regard y as the independent variable and x as the dependent variable an…
$\frac{4x\sec^{2}(y)-\sec(x)}{y\sec(x)\tan(x)-4\tan(y)}$
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find $\frac{dy}{dt}$. $y = e^{cos^{2}(pi t - 2)}$ $\frac{dy}{dt}=square$
$-\pi\sin(2(\pi t - 2))e^{\cos^{2}(\pi t - 2)}$
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find $\frac{dy}{dt}$. $y=(5 + cos 5t)^{-4}$ $\frac{dy}{dt}=square$
$20\sin5t(5+\cos5t)^{-5}$
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complete the sentence by filling in the correct word. features, such as…
enhance
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find $\frac{dy}{dx}$ by implicit differentiation. $7ysin(x^{2}) = 9xsin…
$\frac{9\sin(y^{2}) - 14xy\cos(x^{2})}{7\sin(x^{2})-18xy\cos(y^{2})}$
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find $\frac{dy}{dt}$. $y = csc^{2}6pi t$ $\frac{dy}{dt}=square$
$- 12\pi\csc^{2}(6\pi t)\cot(6\pi t)$
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find $\frac{dy}{dx}$ by implicit differentiation. $7x^{2}+9xy - y^{2}=7…
$\frac{-14x - 9y}{9x - 2y}$
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step 1 the function (h(t)=(t^{4}-1)^{3}(t^{3}+1)^{6}) is a product, and…
The derivative of \((t^{3}+1)^{6}\) is \(6(t^{3}+1)^{5}(3t^{2})\)
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the function $h(t)=(t^{4}-1)^{3}(t^{3}+1)^{6}$ is a product, and so we …
The first blank is \(t^{4}-1\) and the second blank is \(t^{3}\).
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find $\frac{dy}{dt}$ for $y = sin^{2}(3pi t + 7)$. $\frac{dy}{dt}=squar…
$3\pi\sin(6\pi t + 14)$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
A. $y = e^{u}$, where $u = 1 - 10x$; $\frac{dy}{dx}=-10e^{1 - 10x}$
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review the water quality report and then answer the question. georgetow…
to inform residents about the source and content of Georgetown's drinking water
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review the water quality report and then answer the question. georgetow…
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. georgetowns…
residents of Georgetown
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let f and g be the functions in the table below. | x | f(x) | f(x) | g(…
(a) $F^{\prime}(3)=35$ (b) $G^{\prime}(2)=63$
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10. - / 1 points find the derivative of the function. y = x + (x + sin²…
$7[x+(x + \sin^{2}(x))^{5}]^{6}[1 + 5(x+\sin^{2}(x))^{4}(1 + 2\sin(x)\cos(x))]$
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find the derivative of the function. y = x sin(8/x) y(x) =
$\sin(\frac{8}{x})-\frac{8}{x}\cos(\frac{8}{x})$
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find the derivative of the function. g(\\theta)=5\\cos^{4}(\\theta) g(\…
$- 20\cos^{3}(\theta)\sin(\theta)$
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find the derivatives of the following functions. g(x) = 2x^3 - 7x^2 + 9…
$g^\prime(x)=6x^{2}-14x$ $f^\prime(x)=6(6x^{2}-14x)(2x^{3}-7x^{2}+9)^{5}$
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write the composite function in the form f(g(x)). identify the inner fu…
$(f(u),g(x))=(\tan(u),x^{9})$ $\frac{dy}{dx}=9x^{8}\sec^{2}(x^{9})$
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write the composite function in the form ( f(g(x)) ). identify the inne…
$(f(u),g(x))=(\sqrt{u},x^{3}+6)$ $\frac{dy}{dx}=\frac{3x^{2}}{2\sqrt{x^{3}+6}}$
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question 7 of 10 which of the following would not have been an early go…
A. To end the practice of slavery
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
A. $y = e^{u}$, where $u = 1 - 10x$; $\frac{dy}{dx}=-10e^{1 - 10x}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
C. $y = e^{u},u=-21x$; $\frac{dy}{dx}=-21e^{-21x}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
$u = \sec x$, $\frac{dy}{dx}=4\sec^{4}x\tan x$
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write the function below in the form y = f(u) and u = g(x). then find $…
A. $y=\sqrt{u}$ and $u = 3x^{2}+3x + 5$ $\frac{dy}{dx}=\frac{6x + 3}{2\sqrt{3x^{2}+3x + 5}}$
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which of the following is considered to be a limitation of experiment r…
It is very time and labor intensive.
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which of the following is considered to be a limitation of experiment r…
It is very time and labor intensive.
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which of the following is considered to be a limitation of experiment r…
It is very time and labor intensive.
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write the function below in the form y = f(u) and u = g(x). then find $…
A. $y=\sqrt{u}$ and $u = 3x^{2}+3x + 5$ $\frac{dy}{dx}=\frac{6x + 3}{2\sqrt{3x^{2}+3x + 5}}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
$\frac{7}{(5 - \frac{7x}{4})^{5}}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
$2(-1-\frac{2x}{3})^{-4}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
$\frac{dy}{dx}=2(-1-\frac{2x}{3})^{-4}$
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write the function in the form y = f(u) and u = g(x). then find $\frac{…
$u=-1-\frac{2x}{3}$, $\frac{dy}{dx}=2(-1 - \frac{2x}{3})^{-4}$
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write the function below in the form y = f(u) and u = g(x), then find \…
$48(6x + 5)^{7}$
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write the function below in the form y = f(u) and u = g(x), then find $…
C. $f(u)=u^8$, $g(x)=6x + 5$; $\frac{dy}{dx}=48(6x + 5)^7$
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after the fundraiser ends, positive feedback keeps coming in. people ar…
Incorporating diverse perspectives and balancing immediate and long - term needs
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given y = f(u) and u = g(x), find $\frac{dy}{dx}=f(g(x))g(x)$. y = csc …
$(\frac{1}{x^{2}} - 3)\csc(\frac{1}{x}+3x)\cot(\frac{1}{x}+3x)$
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given y = f(u) and u = g(x) below, find $\frac{dy}{dx}=f(g(x))g(x)$. y …
$-(4 - 7\sin x)\cos(4x + 7\cos x)$
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given y = f(u) and u = g(x), find $\frac{dy}{dx}=f(g(x))g(x)$. y = $sqr…
$-\frac{2\sin x}{3\sqrt[3]{\cos x}}$
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which group was opposed to slavery but wanted to avoid a breakup of the…
Anti - slavery Movement
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given y = f(u) and u = g(x), find $\frac{dy}{dx}=f(g(x))g(x)$ for the f…
$3\cos(3x + 2)$
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given y = f(u) and u = g(x), find $\frac{dy}{dx}=f(g(x))g(x)$. y = 3u^8…
$168(7x - 2)^{7}$
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given y = f(u) and u = g(x), find $\frac{dy}{dx}=f(g(x))g(x)$. y = 8u -…
$14x^{6}$
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4. what powers were given to the central government under the articles …
4. The central government could declare war, make peace, negotiate treaties, manage Native - American affairs, issue currency, and borrow money. 5. It had no power to regulate int…
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question 22 find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for …
\(-\frac{5}{x(x + h)}\)
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find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function…
$2x+h + 7$
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find the difference quotient $\frac{f(x + h)-f(x)}{h}$, $h eq0$, for th…
$-9$
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find the difference quotient $\frac{f(x + h)-f(x)}{h}$ for the function…
$2x+h + 5$
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8.3 rates of change and behavior of graphs core: 14.26/22 answered: 17/…
15
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the complete graph of the function is shown, estimate the absolute maxi…
Absolute maximum: 16 Absolute minimum: - 16
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f(x)=3x^{\frac{1}{3}} - x furthest left local extrema: (□,□) furthest r…
Furthest left local extrema: $(-1,-2)$ Furthest right local extrema: $(1,2)$ Increasing on the interval: $(-1,1)$ Decreasing on the interval: $(-\infty,-1)\cup(1,\infty)$
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use the graph below to estimate the local extrema of the function and t…
Local extrema: $(-2,-8)$ Increasing on the interval: $(-2,\infty)$ Decreasing on the interval: $(-\infty,-2)$
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use the intermediate value theorem to confirm that the given polynomial…
$f(1)=-4$ $f(2)=22$ Because $f$ is a polynomial function and since $f(1)$ is negative and $f(2)$ is positive, there is at least one real zero between $x = 1$ and $x = 2$.
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use the graph below to estimate the local extrema of the function and t…
Furthest left local extrema: $(-1,-28)$ Furthest right local extrema: $(3,-10)$ Increasing on the interval: $(-\infty,-1),(1,3)\cup(3,\infty)$ Decreasing on the interval: $(-1,1)$
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what is the difference between human capital and capital goods? based o…
Country 3 is most favorable for entrepreneurs because it has a strong stock market, strong private - property protections, few barriers to starting a new business, and encourages …
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watch the video and then solve the problem given below. click here to w…
$-\sqrt{2}$
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what would happen to the price of oil if the organization of the petrol…
If OPEC decided to produce less oil, the price of oil would likely rise. The economic term is quota.
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question 13 for the following exercise, use a graphing utility to estim…
Furthest left local extrema: $(0,3)$ Furthest right local extrema: (approximate value from graphing utility, corresponding $y$ - value from graphing utility) Increasing on the int…
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the following is the graph of the function f. estimate the intervals wh…
Increasing: $(-6,-2),(3,7)$ Decreasing: $(-2,3)$ Local maximum: $(-2,128)$ Local minimum: $(3,-128)$
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suppose that $f(x)=\frac{9}{ln(x^{3}+2)}$. find $f(3).$ $f(3)=$
$-\frac{243}{29(\ln(29))^{2}}$
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find the derivative of the function $y = e^{(x^{2}-5)^{6}}$ using the c…
$12x(x^{2}-5)^{5}e^{(x^{2}-5)^{6}}$
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find the derivative of the function (y = e^{4x^{2}+3x - 4}) using the c…
$(8x + 3)e^{4x^{2}+3x - 4}$
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find the derivative. y = √(1 + e^{2x})
$\frac{e^{2x}}{\sqrt{1 + e^{2x}}}$
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attempt 1: 10 attempts remaining. evaluate $\frac{d}{dt}(3e^{-11t})$. $…
\(-33e^{-11t}\)
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differentiate: $f(x)=(17x^{3}-5x^{0})^{5/2}$ $f(x)=$
$\frac{255}{2}x^{2}(17x^{3}-5)^{\frac{3}{2}}$
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calculate the derivative of the function. g(x)=(7x^{2}+x + 7)^{-8} g(x)=
$-8(14x + 1)(7x^{2}+x + 7)^{-9}$
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calculate the derivative of the function. $r(x)=(0.2x^{2}-4.9x + 2.6)^{…
$2.6(0.4x - 4.9)(0.2x^{2}-4.9x + 2.6)^{1.6}$
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given $f(x)=(4x^{3}-8x^{2}+3x - 6)^{20}$, find $f(x)$. $f(x)=$
$20(4x^{3}-8x^{2}+3x - 6)^{19}(12x^{2}-16x + 3)$
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find $\frac{dy}{dx}$ if $y = (-8x^{3}+5x^{2}-x)^{5}$. $\frac{dy}{dx}=$
$5(-8x^{3}+5x^{2}-x)^{4}(-24x^{2}+10x - 1)$
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calculate the derivative of the function. $f(x)=(8x - 1)^2$ $f(x)=$
$128x - 16$
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mark the local extrema on the following graph.
Mark a dot at \((-4,36)\) for the local maximum and a dot at \((4,-45)\) for the local minimum.
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home > math - 115 - 70 fall 2025 > assessment 3.3 rates of change and b…
Mark a dot near the point \((-3,15)\) for the local - maximum and a dot near the point \((0,0)\) for the local - minimum.
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3.3 rates of change and behavior of graphs score: 6/22 answered: 6/22 q…
$3(b - 3)$
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3.3 rates of change and behavior of graphs score: 5/22 answered: 5/22 q…
$-\frac{1}{9(h + 9)}$
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the advent of online streaming has led many music listeners to drift aw…
C. most users of the free streaming service were probably encouraged by the restriction to move to a paid version of the service with unlimited, ad - free listening
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3.3 rates of change and behavior of graphs score: 4/22 answered: 4/22 q…
$2h^{2}+18h + 54$
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no matter what youre doing, something else always seems more appealing.…
1. Not knowing the limits of what can be done sometimes allows you to achieve more. 2. Starting from scratch can help you reach an answer. 3. You cannot always see the purpose of …
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what is the solution of 3 + \\frac{x - 3}{2}\\leq4? x\\geq3 x\\leq3 x <…
The solution of the inequality is $x\leq4$.
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question 3 (14.2 points) how do credit scores affect the ability to obt…
d) Higher credit scores lead to better loan terms, lower interest rates, and higher credit limits
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question 20 of 25 read the following summary of the supreme court case …
D. Whether the district had grounds to fear a disruption
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question 12 of 25 the tinker v. des moines supreme court case concerned…
B. Schools have reserved the right to limit expression in past cases and the armbands were, indeed, disruptive.
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3.2.6 quiz: economics and party politics question 9 of 10 what was one …
C. To establish a national bank
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question 9 of 20 read the following excerpt from the great gatsby. i su…
C. Despite his origins, Jay Gatsby became the character he always wanted to become.
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suppose that the function (f) is defined, for all real numbers, as foll…
Yes
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complete the sentence below. on the interval π,2π, the function values …
-1; 1
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complete the sentence below. the domain of both the sine and cosine fun…
Domain: $(-\infty,\infty)$; Range: $[-1,1]$
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john locke would have agreed with all of the following statements excep…
D. Government should have the authority to suppress the will of its citizens if it deems it to be crucial to society.
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which of the following documents was responsible for limiting the power…
A. the Magna Carta
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question 8 0.5 pts from cialdini... your company is launching a new pro…
B. "limited - number"
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by the 1760s, many planters were in debt to british merchant houses. pl…
It limited the money that planters could use to repay debt.
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list the points in the graph in the interval 0 < x < 7 at which the fun…
3,6