Calcul
Limites, dérivées, optimisation et comportement des fonctions.
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the population of a certain inner - city area is estimated to be declin…
\( 375922 \)
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find the limit. (limlimits_{x \to 27} \frac{x - 27}{sqrt{x + 9} - 6})
12
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find the volume of the solid generated by revolving the following regio…
\(\dfrac{88\pi}{3}\)
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example 2: the figure shows the graph of a function g in the xy - plane…
D
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attempt 1: 10 attempts remaining. compute the derivative of the functio…
\( \boldsymbol{-\dfrac{400(x + 1)}{(x^2 + 2x + 4)^9}} \)
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describe the listed aspects of the function. be sure to label and descr…
### 1. Graph The function \( g(x) = x^3 + 2x^2 - x + 4 \) is a cubic (degree 3) polynomial. The leading coefficient is positive (\( 1 \)), so the graph has the characteristic "S -…
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find dy/dx if y = sec(8x²).
\( 16x\sec(8x^{2})\tan(8x^{2}) \)
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find dy/dx if y = sec(8x²)
\( 16x\sec(8x^2)\tan(8x^2) \)
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example 1: the figure shows the graph of a function ( f ) in the ( xy )…
The rates of change of \( f \) at the three labeled points from least to greatest are \( \boldsymbol{f'(B) < f'(A) < f'(C)} \) (or in terms of the points: Rate of change at B, Rat…
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find dy/dx if y = (cscx + 1)^7
\(-7(\csc x + 1)^{6}(\csc x\cot x)\) (corresponding to the orange - colored option: \(-7(\csc x + 1)^{6}(\csc x\cot x)\))
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attempt 1: 10 attempts remaining. compute the derivative of the functio…
\(\frac{5x^{4}-72}{2\sqrt{x^{5}-72x}}\)
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attempt 1: 10 attempts remaining. compute the derivative of the functio…
\( 8(3x + 1)(3x^2 + 2x - 4)^7 \)
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find the following limit or state that it does not exist. assume b is a…
A. \(\lim\limits_{x\to b}\frac{(x - b)^{40}-4x + 4b}{x - b}=-4\)
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4. (4 pts) identify the amplitude, horizontal phase shift, vertical dis…
Amplitude: \( 2 \) Horizontal Phase Shift: \( -\frac{\pi}{6} \) Vertical Displacement: \( 5 \) Period: \( \frac{\pi}{3} \)
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find the following limit or state that it does not exist. \\( \\lim\\li…
-48
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find the following limit or state that it does not exist. \\( \\lim \\l…
\(16(x - 2)\)
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find the following limit or state that it does not exist \\( \\lim\\lim…
A. $\lim\limits_{x\to 2}\frac{x - 2}{\sqrt{4x + 1}-3}=\frac{3}{2}$
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find the following limit or state that it does not exist. \\( \\lim \\l…
$\frac{\sqrt{4x + 1}+3}{4}$
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find the following limit or state that it does not exist $$\\lim_{x \\t…
A. \( \lim\limits_{x \to 4} \frac{\sqrt{x}-2}{x - 4} = \frac{1}{4} \)
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find the following limit or state that it does not exist. (limlimits_{x…
\(\frac{1}{\sqrt{x}+2}\)
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find the following limit or state that it does not exist. (limlimits_{h…
A. \(\lim\limits_{h ightarrow0}\frac{\frac{8}{3 + h}-\frac{8}{3}}{h}=-\frac{8}{9}\)
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find the following limit or state that it does not exist. assume k is a…
A. \(\lim\limits_{w\to -k}\frac{w^2 + 6kw + 5k^2}{w^2 + kw}=-4\)
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find the following limit or state that it does not exist. assume k is a…
\(\frac{w + 5k}{w}\)
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directions: translate each expression. 1. \the sum of a number and 4.\ …
\( x + 4 \) ### 2. "the quotient of a number and -2."
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determine the following limit \\( \\lim\\limits_{x\\to 2} \\frac{x^3 - …
A. \( \lim\limits_{x\to 2}\frac{x^3 - 7x^2 + 6x}{6 - x} = -2 \)
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find the following limit or state that it does not exist (limlimits_{x …
A. \(\lim\limits_{x ightarrow - 1}\frac{x^{2}-3x - 4}{x + 1}=\boxed{-5}\)
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attempt 1: 10 attempts remaining. differentiate: ( f(x) = (17x^3 - 15x^…
\( \boldsymbol{\frac{7}{2}(17x^3 - 15x^6)^{\frac{5}{2}}(51x^2 - 90x^5)} \) (or simplified forms like \( \frac{21}{2}(17x^2 - 30x^5)(17x^3 - 15x^6)^{\frac{5}{2}} \) etc.)
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find the following limit or state that it does not exist (limlimits_{x …
\(x - 4\)
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for the function g(x) shown below, compute the following limits or stat…
B. The limit does not exist.
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for the function g(x) shown below, compute the following limits or stat…
A. $\lim_{x \to 5^+} g(x) = 10$
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is continuous at x = 0. q7(*): describe all points for which the functi…
The function \( f(x)=\frac{1}{x^2 - 1} \) is continuous at all real numbers \( x \) with \( x eq - 1 \) and \( x eq1 \), i.e., the intervals \( (-\infty,-1)\cup(-1,1)\cup(1,+\in…
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for the function g(x) shown below, compute the following limits or stat…
$\lim_{x \to 5^-} g(x) = \boxed{0}$ (so option A with 0)
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for the function g(x) shown below, compute the following limits or stat…
A. \( \lim\limits_{x\to -5^+} g(x) = 0 \)
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for the function g(x) shown below, compute the following limits or stat…
A. \( \lim\limits_{x \to -5^-} g(x) = 0 \)
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let ( f(x) = \begin{cases} x^2 + 4, & x < -4 \\ sqrt{x + 4}, & x geq -4…
$\lim_{x \to -4^-} f(x) = 20$ ### Part b: $\lim_{x \to -4^+} f(x)$
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let ( f(x) = \begin{cases} x^2 + 4, & x < -4 \\ sqrt{x + 4}, & x ge -4 …
A. \(\lim_{x ightarrow - 4^{+}}f(x)=\boldsymbol{0}\) (Simplify your answer)
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let ( f(x) = \begin{cases} x^2 + 4, & x < -4 \\ sqrt{x + 4}, & x geq -4…
A. \( \lim_{x \to -4^+} f(x) = 0 \) ### Part c (if needed, assuming we check the overall limit):
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let f(x)=\\begin{cases} x^2 + 4, & x < -4 \\\\ \\sqrt{x + 4}, & x \\ge …
A. \(\lim_{x ightarrow - 4^{-}}f(x)=\boxed{20}\)
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find the following limit or state that it does not exist. (limlimits_{h…
\(\frac{9}{10}\) (and the correct choice is A)
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find the following limit or state that it does not exist. (lim_{x \to 3…
A. \( \lim\limits_{x \to 3} 1 = \boxed{1} \)
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find the following limit or state that it does not exist. \\(\\lim \\li…
A. \( \lim\limits_{x\to -3} \frac{6x^2 + 7x + 11}{5x - 7} = -2 \)
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assume \\( \\lim_{x \\to 4} f(x) = 6 \\) and \\( \\lim_{x \\to 4} g(x) …
The value of the limit is $3$. The limit laws used are B. Product, E. Sum, G. Root.
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if ( f(x) = llbracket x rbracket + llbracket -x rbracket ), show that (…
- For \( f(a) \) (a is integer): \( 0 \) - For \( \lim_{x ightarrow2^{-}}f(x) \): \( - 1 \) - For \( \lim_{x ightarrow2^{+}}f(x) \): \( - 1 \) - For \( \lim_{x ightarrow2}f(x) \):…
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assume \\( \\lim_{x \\to 5} f(x) = 26 \\), \\( \\lim_{x \\to 5} g(x) = …
The limit laws used are B (Difference) and E (Quotient). So the correct options are: B. Difference E. Quotient
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a farmer has a limited amount of land and must decide whether to use it…
Scarcity
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assume \\( \\lim\\limits_{x \\to 5} f(x) = 26 \\), \\( \\lim\\limits_{x…
13
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15. submit answer practice similar attempt 1: 10 attempts remaining. ca…
\( -8(14x + 1)(7x^2 + x + 7)^{-9} \) (or equivalently \( \frac{-8(14x + 1)}{(7x^2 + x + 7)^{9}} \))
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a) for each of the intervals, find the values of $\\delta d$ and $\\del…
To solve this problem, we need to assume a linear relationship for \( D(t) \) (distance as a function of time) since the average rate of change is constant. Let's assume \( D(t) =…
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intro to economics test economic choice involves: ○ ignoring opportunit…
C. Using scarce resources to fulfill unlimited wants
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intro to economics test scarcity and choice are economic problems faced…
A. wants are unlimited but resources are scarce.
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calculate the derivative of the function. ( r(x) = (0.1x^2 - 4.5x + 2.6…
\( 2.6(0.1x^{2}-4.5x + 2.6)^{1.6}(0.2x - 4.5) \)
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according to the \how to write an essay\ video, what is the benefit of …
A. It organizes the essay structure.
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scarcity is best defined as: the unlimited availability of resources; t…
the limited number of some resources, such as oil
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complete the following for the function ( f(x) = \frac{4x^3 + 3x^2 + 3x…
s: a. The slant asymptote is \(y=\boxed{4x + 3}\) b. There are no vertical asymptotes. c. (Graphing done via utility, with \(f(x)\), \(y = 4x + 3\) plotted, no vertical asymptotes…
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evaluate \\( \\lim_{x \\to \\infty} f(x) \\) and \\( \\lim_{x \\to -\\i…
- $\lim_{x\to\infty} f(x)=\frac{1}{3}$ - $\lim_{x\to-\infty} f(x)=-1$ - Horizontal asymptotes: $y=\frac{1}{3}$ (top) and $y = - 1$ (bottom)
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evaluate \\(\\lim_{x \\to \\infty} f(x)\\) and \\(\\lim_{x \\to -\\inft…
- $\lim_{x\to\infty} f(x)=\boldsymbol{\frac{1}{3}}$ - $\lim_{x\to-\infty} f(x)=\boldsymbol{-1}$ - Horizontal asymptotes: $\boldsymbol{y = \frac{1}{3}}$ and $\boldsymbol{y = -1}$ (…
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the two great points of difference between a democracy and a republic a…
- **Delegation Reason**: "The two great points of difference between a democracy and a republic are first, the delegation of the government, in the latter, to a small number of ci…
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evaluate \\( \\lim_{x \\to \\infty} f(x) \\) and \\( \\lim_{x \\to -\\i…
For \( \lim_{x \to -\infty} f(x) \), the correct choice is A, and \( \lim_{x \to -\infty} f(x) = -1 \)
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activity 1.1.4. for the function given by ( s(t) = 64 - 16(t - 1)^2 ) f…
\( -16h - 32 \) (for \( h eq0 \)) ### Part 2: Average velocity on \([1.5, 2]\)
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evaluate \\( \\lim_{x \\to \\infty} f(x) \\) and \\( \\lim_{x \\to -\\i…
A. \(\lim\limits_{x\to\infty} f(x)=\frac{1}{3}\)
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evaluate \\( \\lim_{x \\to \\infty} f(x) \\) and \\( \\lim_{x \\to -\\i…
For \( \lim_{x \to +\infty} f(x) \), the value is \( \frac{7}{6} \). For horizontal asymptotes, Option A: The top asymptote is \( y = \frac{7}{6} \) and the bottom asymptote is \(…
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1- what are the various definitions of art? why is the definition of ar…
Definitions of art include formalist (focus on form), institutional (art is what art world says), functional (serves a purpose like expression). It changed due to new art forms (d…
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evaluate $\\lim\\limits_{x \\to \\infty} f(x)$ and $\\lim\\limits_{x \\…
For \( \lim_{x \to \infty} f(x) \), the answer is \( \frac{7}{6} \) (Option A). For \( \lim_{x \to -\infty} f(x) \), the limit is \( \frac{-7}{6} \) (Option A with value \( -\frac…
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attempt 1: 10 attempts remaining. given ( f(x) = (7x^3 - 3x^2 + 8x - 5)…
\( 10(21x^{2}-6x + 8)(7x^{3}-3x^{2}+8x - 5)^{9} \)
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determine \\( \\lim\\limits_{x \\to \\infty} f(x) \\) and \\( \\lim\\li…
For \( \lim_{x \to \infty} f(x) \), it is \( \infty \); for \( \lim_{x \to -\infty} f(x) \), it is \( -\infty \). The function has no horizontal asymptotes, so the answer for hori…
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data table one: limiting factors of cricket frogs | limiting factor | b…
For example, the amount of change for High Predators is 30,000 (calculated as 50,000 - 20,000). The formula for amount of change is $ \text{Amount of Change} = \text{Ending Frog C…
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determine ( limlimits_{x \to infty} f(x) ) and ( limlimits_{x \to -inft…
For \(\lim_{x\to\infty} f(x)\), the limit is \(\infty\); for \(\lim_{x\to-\infty} f(x)\), the limit is \(-\infty\). The function has no horizontal asymptotes, so the answer for ho…
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determine \\( \\lim\\limits_{x \\to \\infty} f(x) \\) and \\( \\lim\\li…
for \( \lim_{x \to -\infty} \): A. \( \lim_{x \to -\infty} f(x) = -\infty \) For horizontal asymptotes: Since both \( \lim_{x \to \infty} f(x) = \infty \) and \( \lim_{x \to -\inf…
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determine $\\lim\\limits_{x\\to\\infty} f(x)$ and $\\lim\\limits_{x\\to…
For \(\lim_{x ightarrow\infty}f(x)\), the limit is \(\infty\) (so option A with the box filled as \(\infty\) is incorrect in the sense of finite limit, but following the calculati…
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determine the following limit. \\lim_{w \\to \\infty} \\frac{20w^2 + 2w…
A. \( \lim\limits_{w\to\infty} \frac{20w^2 + 2w + 9}{\sqrt{25w^4 + w^3}} = 4 \)
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question 3 what is the difference between a totalitarian regime and an …
A. A totalitarian regime tries to control citizens' lives more fully than an authoritarian regime.
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attempt 1: 10 attempts remaining. find (\frac{dy}{dx}) if (y = left(-7x…
\( 3(-7x^3 + 9x^2 - x)^2(-21x^2 + 18x - 1) \)
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determine the following limit. (limlimits_{x \to -infty} \frac{19x^3 + …
A. \(\lim\limits_{x\to -\infty}\frac{19x^3 + 8x^2 - 8x}{15x^3 + 7x^2 + 7x + 1}=\frac{19}{15}\)
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determine the following limit at infinity. (limlimits_{x \to infty} \fr…
A. $\lim\limits_{x\to\infty} \frac{5 + 7x + 9x^2}{x^2} = 9$
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determine the following limit. (limlimits_{x \to -infty} (5x^3 - 6x^2 +…
A. \(\lim\limits_{x\to -\infty} (5x^3 - 6x^2 + 1)=\boxed{-\infty}\)
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attempt 1: 10 attempts remaining. calculate the derivative of the funct…
\( 128x - 16 \)
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determine the following limit. (limlimits_{x \to infty} (2x^3 - 8x^2 + …
A. \(\lim\limits_{x\to\infty}(2x^3 - 8x^2 + 1)=\infty\)
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let f(x) = \\(\\frac{x^2 - 9x + 18}{x^2 - 3x}\\) complete parts (a) thr…
A. The graph of \( f \) has one vertical asymptote at \( \boldsymbol{x = 0} \)
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let ( f(x) = \frac{x^2 - 9x + 18}{x^2 - 3x} ). complete parts (a) throu…
\(-1\)
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let ( f(x) = \frac{x^2 - 9x + 18}{x^2 - 3x} ). complete parts (a) throu…
\(-1\)
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find the limit. $lim_{x \\to 0} \\frac{1 + 5x + \\sin x}{4 \\cos x}$
\(\frac{1}{4}\)
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let ( f(x) = \frac{x^2 - 9x + 18}{x^2 - 3x} ). complete parts (a) throu…
\(\lim_{x ightarrow0^-}f(x)=\infty\) (or more precisely \(+\infty\))
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find the limit. (lim_{x \to -2pi} sqrt{x + 13} cos(x + 2pi))
\(\sqrt{13 - 2\pi}\)
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analyze the following limits and find the vertical asymptotes of ( f(x)…
The vertical asymptote(s) occur(s) at \(x = - 12\)
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analyze the following limits and find the vertical asymptotes of ( f(x)…
A. \(\lim\limits_{x ightarrow - 12^{+}}f(x)=\infty\) (or more precisely \(+\infty\))
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find the limit. (limlimits_{y \to -6} (2 - y)^{\frac{7}{3}})
\( 128 \)
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using a graph to determine key features reset analyze the function’s gr…
Over the interval \([-2.5, 0.5]\), the local maximum is 2.
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based on what you have read, what are the three most important facts in…
A. Power comes from the people, C. Citizens of the United States have guaranteed rights, D. Citizens have certain responsibilities and duties
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analyze the following limits and find the vertical asymptotes of ( f(x)…
\(\lim\limits_{x ightarrow - 12^{-}}f(x)=-\infty\)
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graphs using local maximum and local minimum values use the graph to fi…
Over the interval \([-3, 0]\), the local minimum is \(-16.18\). Over the interval \([0, 3]\), the local maximum is \(3.75\). Over the interval \([0, 3]\), the local minimum is \(-…
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analyze the following limits and find the vertical asymptotes of ( f(x)…
### Part b: $\boldsymbol{\lim_{x \to -12^-} f(x)}$ First, simplify $f(x)$: The denominator $x^2 - 144$ factors as $(x - 12)(x + 12)$, so: $$f(x) = \frac{x - 12}{(x - 12)(x + 12)} …
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analyze the following limits and find the vertical asymptotes of ( f(x)…
# Explanation: ## Step1: Simplify the function First, factor the denominator: \(x^2 - 144=(x - 12)(x + 12)\). So \(f(x)=\frac{x - 12}{(x - 12)(x + 12)}\), and for \(x eq12\), we …
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suppose that \\(\\lim\\limits_{x \\to -4} p(x) = 8\\), \\(\\lim\\limits…
-1 ### Part (b)
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if ( a eq 0 ), then ( limlimits_{x \to a} \frac{x^2 - a^2}{x^4 - a^4} )…
\(\frac{1}{2a^2}\)
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analyze the following limits and find the vertical asymptotes of ( f(x)…
### Part b: # Explanation: ## Step 1: Simplify the function We know that \( f(x)=\frac{x - 12}{x^{2}-144}=\frac{x - 12}{(x - 12)(x + 12)}=\frac{1}{x + 12} \) (for \( x eq12 \)). …
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analyze the following limits and find the vertical asymptotes of f(x)=\…
A. \(\lim_{x ightarrow12}f(x)=\frac{1}{24}\)
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analyze the following limits and find the vertical asymptotes of ( f(x)…
\(\frac{1}{x + 12}\)
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determine the following limit, using ∞ or −∞ when appropriate, or state…
A. \(\lim\limits_{x\to 3^{+}}\frac{x^{2}-6x + 8}{x - 3}=-\infty\)
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now, evaluate the limit. select the correct choice below and, if necess…
A. \(\lim\limits_{x\to 4} \frac{4x^2 - 64}{x - 4} = \boxed{32}\)
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suppose that \\(\\lim\\limits_{x\\to -4} p(x) = 8\\), \\(\\lim\\limits_…
\(-1\) (If we follow the given limit values. If the answer 16 is expected, there might be a typo in the problem's limit values)