微積分
極限、導數、最優化與函數性質。
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money matters there are many crucial factors that go into providing a s…
1. Long - term results show improved test scores for students in states that boosted their low - income public school funding. 2. In states that increased aid for low - income dis…
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there are many crucial factors that go into providing a solid education…
Higher - income districts receive a disproportionate amount of funding from local and federal sources. Increasing school funding for low - income districts can narrow the socioeco…
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there are many crucial factors that go into providing a solid education…
States should increase public school funding, especially for low - income districts.
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write the expression in terms of sine and cosine, and simplify so that …
\(1\)
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use trigonometric identities to write sin x in terms of cos x. choose t…
B. \(\sin x=\pm\sqrt{1 - \cos^{2}x}\)
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find the five remaining trigonometic functions of θ. secθ = 5/2, sinθ <…
\(\sin\theta=-\frac{\sqrt{21}}{5}\), \(\cos\theta=\frac{2}{5}\), \(\tan\theta=-\frac{\sqrt{21}}{2}\), \(\csc\theta=-\frac{5\sqrt{21}}{21}\), \(\cot\theta=-\frac{2\sqrt{21}}{21}\)
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find the remaining five trigonometic functions of \\( \\theta \\). \\( …
\(\cos\theta=-\frac{\sqrt{21}}{5}\), \(\tan\theta =-\frac{2\sqrt{21}}{21}\), \(\csc\theta=\frac{5}{2}\), \(\sec\theta=-\frac{5\sqrt{21}}{21}\), \(\cot\theta=-\frac{\sqrt{21}}{2}\)
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identify any extrema of the function by recognizing its given form or i…
relative minimum \((x,y,z)=(-1,6,-28)\); relative maximum: DNE
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identify any extrema of the function by recognizing its given form or i…
relative minimum \((x,y,z)=(0,0,5)\); relative maximum: DNE
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identify any extrema of the function by recognizing its given form or i…
relative minimum \((x,y,z)=(2,3,0)\); relative maximum: DNE
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the arc from point a to the north pole of a planet subtends a central a…
The exact linear velocity is \(\frac{425\sqrt{2}\pi}{2}\) miles per hour and the approximate linear velocity is \(943.5\) miles per hour.
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find all relative extrema and saddle points of the function. use the se…
relative minimum \((x,y,z)=(7,-8,z(7,-8))\) First, find \(z(7,-8)\): \(z(7,-8)=7^{2}+7\times(-8)+\frac{1}{2}\times(-8)^{2}-6\times7+( - 8)\) \(=49-56 + 32-42-8\) \(=49+32-(56 + 42…
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the arc from point a to the north pole of a planet subtends a central a…
The linear velocity is \(942.3\) miles per hour.
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the arc from point a to the north pole of a planet subtends a central a…
\(\frac{\pi}{10}\)
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the blade of a circular saw rotates at a rate of 2000 revolutions per m…
\(43.1\)
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a ferris wheel can carry 800 passengers in 32 capsules around a circle …
\(0.8\)
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find the angular velocity in radians per minute and linear velocity in …
The linear velocity is \(953.9\) inches per minute.
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find the angular velocity in radians per minute and linear velocity in …
\(276.5\)
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a windmill for generating electricity has a blade that is 30 feet long.…
\(45.7\)
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consider the following. $f(x,y)=x^{3}+y^{3}-3x^{2}+9y^{2}+3x+27y+26$ (a…
(a) \((1,-3)\) (c) \((1,-3)\)
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which term defines limited or uncertain access to foods of sufficient q…
a. Food insecurity
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use the graph to determine (a) open intervals on which the function is …
A. The function is increasing on the interval(s) \((1,5)\)
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use the graph to determine (a) open intervals on which the function is …
The function is increasing on the interval \((-\infty,\infty)\)
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find the point on the line $\\frac{x}{5}+\\frac{y}{10}=1$ that is close…
\((\frac{23}{5},\frac{4}{5})\)
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you are designing a rectangular poster to contain 50 in.² of printing w…
\(w = 7\) in.
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use the graph to determine (a) open intervals on which the function is …
A. The function is increasing on the interval(s) \((-\infty,\infty)\)
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use the graph to determine (a) open intervals on which the function is …
The function is increasing on the interval \((-\infty,\infty)\)
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use the graph to determine (a) open intervals on which the function is …
The function is increasing on the interval \((-\infty,\infty)\)
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a rectangular plot of farmland will be bounded on one side by a river a…
The length of the shorter side of the rectangular plot is \(200\space m\). The length of the longer side of the rectangular plot is \(400\space m\).
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a rectangular plot of farmland will be bounded on one side by a river a…
\(80000\) \(m^{2}\)
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use a calculator to find the value in decimal degrees. cos^{-1}(-0.9702…
\(165.0000\)
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use the graph to determine (a) open intervals on which the function is …
A. The function is increasing on the interval(s) \((2,\infty)\)
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complete the statement. y = cos - 1x means that x = ____, for 0 ≤ y ≤ π…
\(\cos y\)
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watch the video and then solve the problem given below. click here to w…
\(\frac{\sqrt{2-\sqrt{2}}}{2}\)
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evaluate the following limit. lim _ { x ightarrow infty } left( 1 + \fr…
$1$
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suppose the graph of ( f ) is given. describe how the graph of each fun…
(a) shift 5 units to the left and 2 units upward (b) shift 4 units to the right and 3 units downward
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which of the following is true of mixed media? a. mixed media is the us…
D. One form of mixed media was commonly used to create illuminated manuscripts.
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4 multiple answer 1 point the logarithmic function ( g(x)=ln x ) is tra…
- \(g(x)\) is translated \(2\) units to the left - \(g(x)\) is translated \(1\) unit downward - The vertical asymptote shifts \(2\) units to the left ### Question 5
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use lhôpitals rule to find the following limit. lim (ln 3x - ln (x + 7)…
$\ln3$
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look at the graph: what is the equation of the vertical asymptote?
\(x = - 6\)
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find the derivative of $y=sqrt{x}ln x$.
\(\frac{\ln x + 2}{2\sqrt{x}}\)
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use the properties of limits to help decide whether the limit exists. i…
A. \(\lim_{x ightarrow\infty}\frac{4x}{5x - 2}=\frac{4}{5}\)
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the function $f(x)$ is graphed below. how many points on the graph repr…
\(1\)
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question the function ( f(x) ) is graphed below. how many points on the…
1
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consider the equation below. (if an answer does not exist, enter dne.) …
(a) Increasing: \((-\infty,-1)\cup(9,\infty)\); Decreasing: \((-1,9)\) (b) Local minimum value: \(-479\); Local maximum value: \(21\) (c) Inflection point: \((4,-229)\); Concave u…
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find the vertical asymptote(s) of the graph of the function. g(x)=\\fra…
A. The function has one vertical asymptote, \(x = 3\).
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fill in the blank with the appropriate axis (x - axis or y - axis). (a)…
(a) \(x\) - axis (b) \(y\) - axis
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use the given graph of ( f ) over the interval ( (0,6) ) to find the fo…
(a) \((0.5,2)\cup(4,6)\) (b) \((0,0.5)\cup(2,4)\) (c) \((3,6)\) (d) \((0,3)\) (e) \((3,2)\)
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example 3 to illustrate the mean value theorem with a specific function…
\(c^{2}=\frac{16}{3}\), \(c=\pm\frac{4}{\sqrt{3}}\) and the valid \(c\) in \((0,4)\) is \(c = \frac{4}{\sqrt{3}}\)
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use lhôpitals rule to find the following limit lim (2 sec x - 2 tan x) …
\(0\)
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why is manufacturing considered a secondary industry? it transforms raw…
It transforms raw materials into finished goods.
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find the following limit. \\( \\lim _ { x \ ightarrow 0 ^ { + } } x ^ {…
\(0\)
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18 multiple choice 1 point determine the sign (positive or negative) of…
18. B. Positive 19. A. Positive
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16 multiple choice 1 point determine the sign (positive or negative) of…
16. Positive 17. Negative
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evaluate trig values of quadrant angles in degree use unit circle to ev…
-1
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evaluate without using a calculator by using ratios in a reference tria…
\(-\sqrt{2}\) (corresponding to the second option in the multiple - choice list)
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structional video then use the problems to the right to practice and le…
\(-\frac{\sqrt{2}}{2}\)
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6 multiple choice 1 point give the exact value. cos 30° √3/2 2√3/3 √3 √…
\(\frac{\sqrt{3}}{2}\)
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4 multiple choice 1 point give the exact value. cos 45° 5 multiple choi…
For \(\cos45^{\circ}\): \(\frac{\sqrt{2}}{2}\) (the fourth option). For \(\sec150^{\circ}\): \(-\frac{2\sqrt{3}}{3}\) (the second option).
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multiple choice 1 point give the exact value. sec 210° 2√3/3 -√2 -2√3/3…
1. \(-\frac{2\sqrt{3}}{3}\) 2. \(-2\)
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10 multiple choice 1 point find the exact value of ( sin left(-\frac{5 …
$-\frac{1}{2}$ (corresponding to the first option)
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multiple choice 1 point evaluate without using a calculator by using ra…
\(\frac{1}{2}\)
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hen use the problems to the right to practice and learn the concepts. l…
\(\frac{1}{2}\)
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multiple choice 1 point give the exact value. $\tan \frac{pi}{4}$ $sqrt…
1
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5 multiple choice 1 point give the exact value. tan 300° -√3/3 √3 -√3 √…
\(-\sqrt{3}\) (the option with \(-\sqrt{3}\))
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2 multiple choice 1 point give the exact value. $\\cos 210^{\\circ}$ $\…
\(-\frac{\sqrt{3}}{2}\)
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question the function ( f(x) ) is defined below. what is the end behavi…
The degree of the polynomial is \(3\), and the leading coefficient is \(-7\). The correct pair of limits is \(\lim_{x\to-\infty}f(x)=\infty,\ \lim_{x\to\infty}f(x)=-\infty\) (the …
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question the function ( f(x) ) is defined below. what is the end behavi…
The degree of the polynomial is \(5\), and the leading coefficient is \(3\). The correct pair of limits is \(\lim_{x ightarrow-\infty}f(x)=-\infty,\lim_{x ightarrow\infty}f(x)=\in…
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question 3 of 10 which person is being selfless? a. aure, who volunteer…
A. Aure, who volunteers at a local hospital
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answer as ( x ightarrow-infty, f(x) ightarrow-infty ) and as ( x ightar…
as \( x \to -\infty, f(x) \to -\infty \) and as \( x \to \infty, f(x) \to -\infty \)
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use transformations of ( f(x)=sqrt{x} ) to graph the following function…
B. The graph of \(f(x)=\sqrt{x}\) should be shifted 4 units down.
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$$ lim _ { x ightarrow 0 } \frac { 3 sin x } { x } = $$
\(3\)
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the function $f(x)$ is graphed below. how many points on the graph repr…
\(0\)
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use lhôpitals rule to find the following limit. \\( \\lim _ { x \ ighta…
\(1\)
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which best explains a major dissatisfaction of the merchant class with …
B. There was no provision for a uniform currency.
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how does the eighth amendment protect people found guilty of a crime? i…
It limits the punishment they can receive.
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question 6 2.5 pts greta wants to do a study on how self - efficacy cha…
cross - sectional
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use lhopitals rule to find the limit. $$\\lim_{x \\to 0} \\frac{x 11^{x…
\(\frac{1}{\ln11}\)
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use lhôpitals rule to find the limit of $limlimits_{\theta\to0}\frac{2^…
\(\frac{\ln2}{4}\)
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if ( k(x)=\frac{x^{3}+512}{x + 8} ), complete the table and use the res…
| \(x\) | \(-8.1\) | \(-8.01\) | \(-8.001\) | \(-7.999\) | \(-7.99\) | \(-7.9\) | | ---- | ---- | ---- | ---- | ---- | ---- | ---- | | \(k(x)\) | \(194.441\) | \(162.400\) | \(192…
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officials in a certain region tend to raise the sales tax in years in w…
A. \(\lim_{x\to2009}T(x)=7.5\) cent(s)
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use the properties of limits to help decide whether the limit exists. i…
A. \(\lim_{x ightarrow\infty}\frac{3x^{3}+8x - 5}{8x^{4}-9x^{3}-2}=0\)
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use the properties of limits to help decide whether each limit exists. …
A. \(\lim_{x ightarrow\infty}\frac{2x^{2}+2x}{7x^{2}-2x + 1}=\frac{2}{7}\)
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decide from the graph whether each limit exists. if a limit exists, est…
(a) A. \(\lim_{x ightarrow - 6}F(x)=-4\) (b) B. The limit does not exist.
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decide from the graph whether each limit exists. if a limit exists, est…
A. \(\lim_{x ightarrow - 6}F(x)=-2\)
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lim f(x)=4 and lim f(x)=4, but f(6)= -4. x→6^- x→6^+ what can you say a…
B. is 4
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consider the function $f(x)=\frac{-1}{-6x + 9}$. simplify the differenc…
\(\frac{-6}{(6x + 6h-9)(6x-9)}\)
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use the graph below to find the average rate of change of the function …
\(0\)
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graph the function ( f(x)=-x^{2}+2x ) by starting with the graph of ( y…
The graph of \(y=-x^{2}+2x\) is obtained by reflecting the graph of \(y = x^{2}\) about the \(x\) - axis, then shifting it 1 unit to the right and 1 unit up.
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find the derivative of $f(x)=e^{x}cos x$.
\(f^\prime(x)=e^{x}(\cos x - \sin x)\)
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find the derivative of ( h(x) = e^{x^{2}-3x} ).
\( h^{\prime}(x)=(2x - 3)e^{x^{2}-3x} \)
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find the derivative of $h(x)=\\ln(x^{2}-3x)$. 1 $h(x)=\\frac{1}{2x - 3}…
None of the given options (Option 1: \(h^\prime(x)=\frac{1}{2x - 3}\) and Option 2: \(h^\prime(x)=\frac{1}{x^{2}-3x}\)) are correct. The correct derivative is \(h^\prime(x)=\frac{…
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the derivative of f(x) = 5 cos(2 - 3x) is f(x) = c sin(2 - 3x). find th…
\(15\)
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difficulty: 11 the derivative of ( f ( x ) = 3 sin ( 2 x - 1 ) ) is ( f…
\(3\)
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the derivative of ( f(x)=12 ln sqrt3{1-2 x} ) is ( f^{prime}(x)=\frac{c…
\(c = 8\)
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the derivative of $y = 7ln\frac{1}{2 - 3x}$ is $\frac{dy}{dx}=\frac{2}{…
\( 21 \)
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the derivative of ( f(x)=\frac{ln (6 x+5)}{3} ) is ( f^{prime}(x)=\frac…
\(2\)
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the derivative of $f(x)=(e^{x}+e^{-x})(e^{x}-e^{-x})$ is $f(x)=\\frac{2…
\(4\)
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4 the derivative of y = 3e^{6x} is \\frac{dy}{dx}=\\frac{e^{6x}}{c}. fi…
\(2\)
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the derivative of ( f(x) = 3e^{2x + 1} ) is ( f(x) = ce^{2x + 1} ). fin…
\(c = 6\)