Exam 12: Limits, Derivatives, and Definite Integrals

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3} \frac{x^{2}+4 x-21}{x-3}$

Free

(Short Answer)

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Question 1

Correct Answer:

Verified

10

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

Free

(Short Answer)

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Question 2

Correct Answer:

Verified

2

$\lim _{x \rightarrow 4^{-}} \frac{|x-4|}{x-4}$

Free

(Short Answer)

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Question 3

Correct Answer:

Verified

-1

$\lim _{x \rightarrow-2^{+}}\left(x^{2}+7\right)$

(Short Answer)

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Question 4

Use a calculator to estimate $f^{\prime}(1)$ , where $f(x)=\frac{e^{2 x}}{x}$ .

(Short Answer)

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Question 5

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-2} \frac{x^{2}+8 x+4}{8-x^{2}}$

(Short Answer)

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Question 6

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{1-\cos ^{2} x}{x^{2}}$

(Short Answer)

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Question 7

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

(Short Answer)

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Question 8

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 2} \frac{x^{2}-4 x+5}{3-x^{2}}$

(Short Answer)

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Question 9

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin ^{2} x}{x^{2}}$

(Short Answer)

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Question 10

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

(Short Answer)

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Question 11

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 7} \frac{3 x^{2}-21 x}{x-7}$

(Short Answer)

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Question 12

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-1} \frac{x^{2}-2 x+4}{x^{2}-3}$

(Short Answer)

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Question 13

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

(Short Answer)

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Question 14

Find the equation of the tangent line to the graph of $f(x)=\frac{2}{x}$ at the point $(1,2)$ .

(Short Answer)

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Question 15

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{3 x-2}{2 x+3}$

(Short Answer)

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(31)

Question 16

Find the slope of the tangent line to the graph of $f(x)=5 x^{2}-3$ at the point where $x=1$ .

(Short Answer)

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(40)

Question 17

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

(Short Answer)

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(43)

Question 18

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{5 x^{3}+1}{x^{2}+3 x-2}$

(Short Answer)

4.9/5

(30)

Question 19

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \sqrt{2 x^{2}-1}$

(Short Answer)

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Question 20

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3} \frac{x^{2}+4 x-21}{x-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

$\lim _{x \rightarrow 4^{-}} \frac{|x-4|}{x-4}$

$\lim _{x \rightarrow-2^{+}}\left(x^{2}+7\right)$

Use a calculator to estimate $f^{\prime}(1)$ , where $f(x)=\frac{e^{2 x}}{x}$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-2} \frac{x^{2}+8 x+4}{8-x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{1-\cos ^{2} x}{x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 2} \frac{x^{2}-4 x+5}{3-x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin ^{2} x}{x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 7} \frac{3 x^{2}-21 x}{x-7}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-1} \frac{x^{2}-2 x+4}{x^{2}-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

Find the equation of the tangent line to the graph of $f(x)=\frac{2}{x}$ at the point $(1,2)$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{3 x-2}{2 x+3}$

Find the slope of the tangent line to the graph of $f(x)=5 x^{2}-3$ at the point where $x=1$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{5 x^{3}+1}{x^{2}+3 x-2}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \sqrt{2 x^{2}-1}$

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Reference: Basic Algebraic Concepts

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Exam 12: Limits, Derivatives, and Definite Integrals

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→3x2+4x−21x−3\lim _{x \rightarrow 3} \frac{x^{2}+4 x-21}{x-3}limx→3​x−3x2+4x−21​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→∞f(x)\lim _{x \rightarrow \infty} f(x)limx→∞​f(x)

lim⁡x→4−∣x−4∣x−4\lim _{x \rightarrow 4^{-}} \frac{|x-4|}{x-4}limx→4−​x−4∣x−4∣​

lim⁡x→−2+(x2+7)\lim _{x \rightarrow-2^{+}}\left(x^{2}+7\right)limx→−2+​(x2+7)

Use a calculator to estimate f′(1)f^{\prime}(1)f′(1) , where f(x)=e2xxf(x)=\frac{e^{2 x}}{x}f(x)=xe2x​ .

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→−2x2+8x+48−x2\lim _{x \rightarrow-2} \frac{x^{2}+8 x+4}{8-x^{2}}limx→−2​8−x2x2+8x+4​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→01−cos⁡2xx2\lim _{x \rightarrow 0} \frac{1-\cos ^{2} x}{x^{2}}limx→0​x21−cos2x​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→4+f(x)\lim _{x \rightarrow 4^{+}} f(x)limx→4+​f(x)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→2x2−4x+53−x2\lim _{x \rightarrow 2} \frac{x^{2}-4 x+5}{3-x^{2}}limx→2​3−x2x2−4x+5​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→0sin⁡2xx2\lim _{x \rightarrow 0} \frac{\sin ^{2} x}{x^{2}}limx→0​x2sin2x​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→4+f(x)\lim _{x \rightarrow 4^{+}} f(x)limx→4+​f(x)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→73x2−21xx−7\lim _{x \rightarrow 7} \frac{3 x^{2}-21 x}{x-7}limx→7​x−73x2−21x​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→−1x2−2x+4x2−3\lim _{x \rightarrow-1} \frac{x^{2}-2 x+4}{x^{2}-3}limx→−1​x2−3x2−2x+4​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→∞f(x)\lim _{x \rightarrow \infty} f(x)limx→∞​f(x)

Find the equation of the tangent line to the graph of f(x)=2xf(x)=\frac{2}{x}f(x)=x2​ at the point (1,2)(1,2)(1,2) .

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→−∞3x−22x+3\lim _{x \rightarrow-\infty} \frac{3 x-2}{2 x+3}limx→−∞​2x+33x−2​

Find the slope of the tangent line to the graph of f(x)=5x2−3f(x)=5 x^{2}-3f(x)=5x2−3 at the point where x=1x=1x=1 .

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→∞f(x)\lim _{x \rightarrow \infty} f(x)limx→∞​f(x)

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→−∞5x3+1x2+3x−2\lim _{x \rightarrow-\infty} \frac{5 x^{3}+1}{x^{2}+3 x-2}limx→−∞​x2+3x−25x3+1​

find the value of the given limit if it exists. If the function approaches ∞\infty∞ or −∞-\infty−∞ , say so. - lim⁡x→52x2−1\lim _{x \rightarrow 5} \sqrt{2 x^{2}-1}limx→5​2x2−1​

Linear Functions, Equations, and Inequalities

Analysis of Graphs of Functions

Polynomial Functions

Rational, Power, and Root Functions

Inverse, Exponential, and Logarithmic Functions

Systems and Matrices

Analytic Geometry and Nonlinear Systems

The Unit Circle and Functions of Trigonometry

Trigonometric Identities and Equations

Applications of Trigonometry and Vectors

Further Topics in Algebra

Reference: Basic Algebraic Concepts

Filters

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 3} \frac{x^{2}+4 x-21}{x-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

$\lim _{x \rightarrow 4^{-}} \frac{|x-4|}{x-4}$

$\lim _{x \rightarrow-2^{+}}\left(x^{2}+7\right)$

Use a calculator to estimate $f^{\prime}(1)$ , where $f(x)=\frac{e^{2 x}}{x}$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-2} \frac{x^{2}+8 x+4}{8-x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{1-\cos ^{2} x}{x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 2} \frac{x^{2}-4 x+5}{3-x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 0} \frac{\sin ^{2} x}{x^{2}}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 4^{+}} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow 4^{+}} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 7} \frac{3 x^{2}-21 x}{x-7}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-1} \frac{x^{2}-2 x+4}{x^{2}-3}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

Find the equation of the tangent line to the graph of $f(x)=\frac{2}{x}$ at the point $(1,2)$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{3 x-2}{2 x+3}$

Find the slope of the tangent line to the graph of $f(x)=5 x^{2}-3$ at the point where $x=1$ .

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow \infty} f(x)$ $find the value of the given limit if it exists. If the function approaches \infty or -\infty , say so. - \lim _{x \rightarrow \infty} f(x)$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow-\infty} \frac{5 x^{3}+1}{x^{2}+3 x-2}$

find the value of the given limit if it exists. If the function approaches $\infty$ or $-\infty$ , say so. - $\lim _{x \rightarrow 5} \sqrt{2 x^{2}-1}$