微積分
極限、導関数、最適化、関数挙動。
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find the limits in a), b), and c) below for the function f(x) = \\frac{…
a) $-\infty$ b) $\infty$ c) B. The limit does not exist and is neither $-\infty$ nor $\infty$.
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refer to the graph of y = f(x) to the right to describe the behavior of…
A. $\lim_{x ightarrow1^{-}}f(x)=2$
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for the function shown below, find (if the quantity exists) (a) $lim_{x…
A. $\lim_{x ightarrow0^{+}}f(x)=15$ (B) $\lim_{x ightarrow0^{-}}f(x)=15$ (C) $\lim_{x ightarrow0}f(x)=15$ (D) $f(0)=15$
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assignment submission for this assignment, you submit answers by questi…
$3\ln\frac{8}{3}$
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assignment submission for this assignment, you submit answers by questi…
$\ln\frac{5}{16}$
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use the graph of the function f shown to estimate the indicated quantit…
(Without the actual graph, we can't give a specific number. But if we assume we can read from the graph and the function approaches \(y = 2\) as \(x\to1^{-}\)) A. \(\lim_{x\to1^{-…
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use the graph of the function f shown to the right to estimate the indi…
(D) If there is a solid - dot at x=-2 on the graph, then A. f(-2)= [the y - value of the solid - dot]. If there is a hole or no defined value at x = - 2 on the graph, then B. The …
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given the function $y = \frac{1 - x}{2x^{3}-5}$, find $\frac{dy}{dx}$ i…
$\frac{4x^{3}-6x^{2}+5}{(2x^{3}-5)^{2}}$
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give a limit expression that describes the left end behavior of the fun…
A. $\lim_{x\to-\infty}\frac{9 + 5x+5x^{3}}{x^{3}}=5$
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find each function value and limit. use -∞ or ∞ where appropriate. f(x)…
(B) - 0.061 (C) 0
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an object moves along the y - axis (marked in feet) so that its positio…
a. $v = 3x^{2}-24x + 36$ b. 15 feet per second c. $x = 2$ seconds and $x = 6$ seconds
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find the indicated derivative. $\frac{dy}{dx}$ for $y = x^{3}$ $\frac{d…
$3x^{2}$
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the graph of the following function has one relative extreme - point. f…
\((-2,1)\) (a relative minimum since \(f^{\prime\prime}(x)>0\) at \(x=-2\))
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the graph of the function has one relative extreme - point. plot this p…
$-2$
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find each limit. use -∞ or ∞ when appropriate. f(x)=\\frac{7x - 7}{(x -…
(A) A. \(\lim_{x\to7^{-}}f(x)=\infty\) (B) \(\lim_{x\to7^{+}}f(x)=\infty\) (C) \(\lim_{x\to7}f(x)=\infty\)
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find the limits in a) through c) below for the function (f(x)=\frac{x^{…
a) The question seems incomplete as the limit value for part a) is not clearly stated. b) A. $\lim_{x\to - 10^{+}}f(x)=\infty$ c) The limit does not exist and is neither $-\infty$…
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find the limits in a) through c) below for the function $f(x)=\frac{x^{…
a) A. \(\lim_{x\to - 10^{-}}f(x)=-\infty\) b) A. \(\lim_{x\to - 10^{+}}f(x)=\infty\)
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find the limits in a) through c) below for the function f(x) = \\frac{x…
A. $\lim_{x\to - 10^{-}}f(x)=-\infty$
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find (a) the leading term of the polynomial, (b) the limit as x approac…
(A) $x^{7}$ (B) $\infty$ (C) $-\infty$
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describe the end behavior of the function f(x)=3x^2 + 4x^3+15 by findin…
$\lim_{x ightarrow-\infty}f(x)=-\infty$
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describe the end behavior of the function f(x)=3x^2 + 4x^3+15 by findin…
\(\infty\)
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find each function value and limit. use - ∞ or ∞ where appropriate. f(x…
-0.139
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find each function value and limit. use - ∞ or ∞ where appropriate. f(x…
(A) $f(10)\approx1.362$ (B) $f(100)\approx1.215$ (C) $\lim_{x ightarrow\infty}f(x)=1.2$
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given the function y = (2 + 4x^2 - 5x) (-3x^3 + 5), find $\frac{dy}{dx}…
$\frac{dy}{dx}=-60x^{4}+60x^{3}-18x^{2}+40x - 25$
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because great britains debt nearly doubled during the french and indian…
- British action: establish new trade regulations that made legally traded goods cheaper than illegally traded goods; Desired result: reduce illegal trade - British action: impose…
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question given the function $f(x)=(1 + 10x-5x^{-1})(4x^{-2}-9)$, find $…
$60x^{-4}-8x^{-3}-85x^{-2}-90$
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use the graph of the function f shown to estimate the indicated limits …
A. \(\lim_{x\to0^{+}}f(x)= - 5\)
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function cosine function: (f(x)=cos x) sketch of graph write using inte…
- Intervals of increasing: \(\bigcup_{k = -\infty}^{\infty}[2k\pi-\pi,2k\pi]\) - Intervals of decreasing: \(\bigcup_{k=-\infty}^{\infty}[2k\pi,2k\pi + \pi]\) - Left - end behavior…
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if $f(x)=cos x - 6\tan x$, then $f(x)=$ $f(2)=$
$f'(x)=-\sin x - 6\sec^{2}x$ $f'(2)\approx - 35.571$
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find the limit if it exists. \\(\\lim_{x\\to7}4x\\) select the correct …
A. $\lim_{x ightarrow7}4x = 28$
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find the given limit. lim(x→ - 7) (x^2 - 2)/(7 - x) select the correct …
A. $\lim_{x ightarrow - 7}\frac{x^{2}-2}{7 - x}=\frac{47}{14}$
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question given the function $y = (-5 - 6x^{-1})(-1 + 10x^{-1}+9x^{2})$,…
$44x^{-2}-90x + 120x^{-3}-54$
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question 8 in which of these instances does a loss occur for a business…
When expenses are greater than revenues
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the graph of the function f is shown below. if m is the slope of the li…
\(m>0\)
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find each indicated quantity if it exists. let f(x) = { x², for x < - 2…
(A) $\lim_{x\to - 2^{-}}f(x)=4$ (C) B. The limit does not exist. (D) B. The function is not defined at $x=-2$.
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if $f(x)=6sin x + 5cos x$, then $f(x)=-6cos x - 5sin x$
$6\cos x - 5\sin x$
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function sine function: f(x)=sin x sketch of graph write using interval…
- Intervals of increasing: \((2k\pi-\frac{\pi}{2},2k\pi+\frac{\pi}{2})\), \(k\in\mathbb{Z}\) - Intervals of decreasing: \((2k\pi+\frac{\pi}{2},2k\pi+\frac{3\pi}{2})\), \(k\in\math…
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find each indicated quantity if it exists. let f(x) = {x², for x < - 2;…
C. B. The limit does not exist.
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use the bisection method to approximate, accurate to two decimal places…
$1.25$
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the graph of the function f is shown below. which statement best descri…
$f^{\prime}(-7)=0$
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find each indicated quantity if it exists. let f(x) = {x^2, for x < - 2…
(A) A. $\lim_{x ightarrow - 2^{+}}f(x)=-4$ (B) A. $\lim_{x ightarrow - 2^{-}}f(x)=4$
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find each indicated quantity if it exists. let f(x) = { x^2, for x < - …
A. $\lim_{x ightarrow - 2^{+}}f(x)=-4$
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the graph of the function f is shown below. which statement best descri…
$f'(-7)$ is a small negative number.
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let f(x) = { (x^2 - 144)/(x + 12) if x < 0, (x^2 - 144)/(x - 12) if x >…
a) A. \(\lim_{x ightarrow - 12}f(x)=-24\) b) The limit does not exist. c) \(\lim_{x ightarrow12}f(x)=24\)
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let (f(x)=\frac{x - 6}{x^{2}-6x}). find the indicated quantities, if th…
(A) B. The limit does not exist (B) \(\frac{1}{6}\) (C) \(\frac{1}{36}\)
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let f(x) = \\frac{x^{2}-3x - 10}{x - 5}. find a) \\lim_{x\\to5}f(x), b)…
a) A. $\lim_{x ightarrow5}f(x)=7$ b) $\lim_{x ightarrow0}f(x)=2$ c) $\lim_{x ightarrow - 2}f(x)=0$
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find lim h→0 (f(5 + h) - f(5))/h if f(x)= - 7x - 1. lim h→0 (f(5 + h) -…
-7
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find $lim_{h ightarrow0}\frac{f(4 + h)-f(4)}{h}$ if $f(x)=x^{2}+2$. $li…
8
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find the limit if it exists. \\(\\lim_{x\\to6}2x\\) select the correct …
A. \(\lim_{x ightarrow6}2x = 12\)
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the graph of the function g on the closed interval 0, 9 consists of fou…
C. 10
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find the limit if it exists. \\(\\lim_{x\\to - 1}(10x + 9)\\) a. (10cdo…
A. $\lim_{x ightarrow - 1}(10x + 9)=-1$
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find the limit if it exists. lim(x→ - 1)(10x + 9) which of the followin…
D. $10\cdot\lim_{x ightarrow - 1}x+\lim_{x ightarrow - 1}9$
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find the limit if it exists. \\(\\lim_{x\\to8}x(x - 4)\\) a. \\((\\lim_…
B. $\lim_{x ightarrow8}x\cdot(\lim_{x ightarrow8}x-\lim_{x ightarrow8}4)$ A. $\lim_{x ightarrow8}x(x - 4)=32$
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find the limit if it exists. \\(\\lim_{x\\to8}x(x - 4)\\) which of the …
B. $\lim_{x ightarrow 8}x\cdot(\lim_{x ightarrow 8}x-\lim_{x ightarrow 8}4)$
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find the horizontal asymptote, if any, of the graph of the rational fun…
A. The horizontal asymptote is $y = 3$
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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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use the graph of the rational function to complete the following statem…
1
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a marine manufacturer will sell n(x) power boats after spending $x thou…
(A) $N^\prime(x)=\frac{3810}{x^{2}}$ (B) $N^\prime(10) = 38.1$, which means when advertising spending is $10,000, the number of boats sold is increasing at a rate of 38.1 boats pe…
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the total sales of a company (in millions of dollars) t months from now…
(A) $S'(t)=0.03t^{2}+t + 8$ (B) $S(5)=59.75$, $S'(5)=13.75$ (C) For $S(8)=107.12$, the total sales 8 months from now will be $\$107.12$ million; for $S'(8)=17.92$, in 8 months the…
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the total sales of a company (in millions of dollars) t months from now…
(A) $S'(t)=0.03t^{2}+t + 8$ (B) $S(5)=59.75$, $S'(5)=13.75$ (C) A. The total sales 8 months from now will be $107.12$ million dollars.
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find f(x) if f(x) = (6x + 4)^2. f(x) = □
$72x + 48$
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the function f(x) has a domain of (-∞, ∞) and a second - derivative giv…
\(-10,2\)
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if an object moves along the y - axis (marked in feet) so that its posi…
(A) $v(x)=192 - 32x$ (B) When $x = 0$, $v = 192$ feet/sec; when $x = 4$, $v = 64$ feet/sec (C) $x = 6$ seconds
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find h(t) if h(t) = \\frac{9}{t^{2/5}} - \\frac{4}{t^{1/2}}. h(t)=□
$-\frac{18}{5t^{\frac{7}{5}}}+\frac{2}{t^{\frac{3}{2}}}$
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find g(w) if g(w) = \\frac{2}{5w^{4}}+7\\sqrt4{w}. g(w) =
$-\frac{8}{5w^{5}}+\frac{7}{4w^{\frac{3}{4}}}$
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if (f(x)=6sin x + 5cos x), then (f(x)=-6cos x - 5sin x) (f(1)=)
$-0.9657$
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find y if y = \\frac{2}{3x^{3}}. y = □
$-\frac{2}{x^{4}}$
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find the indicated derivative. $\frac{d}{dx}\frac{15x + 36}{x}$ $\frac{…
$-\frac{36}{x^{2}}$
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let f(x)=x^4 - 6x^3+12x^2. find (a) the intervals on which f is increas…
(a) Increasing interval: \((0,\infty)\); Decreasing interval: \((-\infty,0)\) (b) Concave up intervals: \((-\infty,1),(2,\infty)\); Concave down interval: \((1,2)\) (c) \(x\) - co…
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find y for y = 7x^{-2}+2x^{-1} y = square
$-14x^{-3}-2x^{-2}$
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6 mark for review which of the following is an antiderivative of (f(x)=…
D. $\int_{0}^{x}\tan(e^{t}+\frac{\pi}{2})dt$
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5 mark for review f(x)=\begin{cases}-1&\text{for }0leq x < 3\\1&\text{f…
A. 5
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find $\frac{dy}{dx}$. y = x^{-6} $\frac{dy}{dx}=square$
$-6x^{-7}$
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let (f(x)=-2x(x - 1)). then (f(0)=) and after simplifying (f(x)=) hint:…
\(f^\prime(0)=2\) \(f^\prime(x)=-4x + 2\)
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find $\frac{d}{dx}x^{5}$. $\frac{d}{dx}x^{5}=square$
$5x^4$
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find f(x) for f(x) = 4. f(x) = □
0
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determine the intervals on which the graph of the function g(t)=3t^4 + …
Concave up: $(-\infty,-3),(0,\infty)$ Concave down: $(-3,0)$
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if $int_{-1}^{1}f(x)dx = 7$ and $int_{-1}^{1}g(x)dx=-9$, then $int_{-1}…
C. 23
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selected values of the twice - differentiable function g are given in t…
B. $-3.647$
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if $h(x)=4 - 2x^{3}$, find $h(2)$. use this to find the equation of the…
$h'(2)=-24$ $m=-24$ $b = 36$
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if (f(x)=4x^{2}-4x + 4), find (f(4)). use this to find the equation of …
$f'(4)=28$ $m = 28$ $b=-60$
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let (f(x)=-6x^{4}sqrt{x}+\frac{3}{x^{3}sqrt{x}}). (f^{prime}(x)=)
$-27x^{\frac{7}{2}}-\frac{21}{2x^{\frac{9}{2}}}$
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find the local maxima and minima for the following function: f(x)=-x^3 …
Local maxima: $5$; Local minima: $1$
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drag the missing word into place. third person narration could be objec…
limited perspective
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find the relative maximas and minimas of each polynomial. f(x)=x^4 + 6x…
Maxima: 0.1 Maxima: Minima: - 338 Minima: 2
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document 4: constitution, article ii, section 1 (1787) \the executive p…
1. The President's role under the Constitution is more powerful and defined compared to leadership under the Articles of Confederation. The Articles had a weak central government …
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selected values of the twice - differentiable function $g$ are given in…
B. $-3.647$
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if $f(x)=4 + 7x-2x^{2}$, find $f(-3)$.
$19$
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drag the right word to its definition a type of third person writing wh…
omniscient third person
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i didnt like the narration in this story. i wanted to hear about at lea…
objective third person
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find the relative maximas and minimas of each polynomial. (f(x)=-x^{4}+…
Maxima: \(-1.4,4.8\); Maxima: \(1,1\); Minima: \(0.4,0.2\)
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i think stories told in are a little spooky! how can any one narrator k…
omniscient third person
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drag the right word to its definition a type of third person writing wh…
objective third person
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drag the right word to its definition a type of third person writing wh…
limited third person
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find the derivative of the function. y = \\sqrt9{x^{2}}-x^{\\sqrt{2}}
$y'=\frac{2}{9x^{\frac{7}{9}}}-\sqrt{2}x^{\sqrt{2}-1}$
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let $f$ be a differentiable function such that $f(1)=2$ and $f(x)=sqrt{…
C. 10.790
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find the inflection points of (f(x)=3x^{4}+41x^{3}-21x^{2}+13). (give y…
$\frac{1}{6},-7$
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if (h(x)=int_{-\frac{pi}{4}}^{sin^{2}x}csc(t^{4}+1)dt) for (-\frac{pi}{…
D. $(2\sin x\cos x)(\csc(\sin^{8}x + 1))$
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determine the open intervals on which the function is increasing, decre…
Increasing: $(-\infty,\infty)$ Decreasing: DNE Constant: DNE