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Archive / Math

Limits & Continuity

Problem 701

Evaluate the limit using L'Hospital's rule $\lim _{x \rightarrow 0} \frac{3^{x}-4^{x}}{x}$

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Problem 702

Name: $\qquad$ Part 1. Multiple Choice Graphing Calculator Permitted. Select the correct answer for each problem. Be sure to fill out the answer sheet on the back of the test. (a) $-\frac{9}{2}$ (b) -4 (c) 4 (d) $\frac{9}{2}$

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Problem 703

Find the limit: $\lim _{x \rightarrow 1} \frac{x}{\ln x}$ .

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Problem 704

Find the limit: $\lim _{x \rightarrow e}(x \ln x - x)$ .

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Problem 705

Calculate the limit: $\lim _{x \rightarrow e}(x \ln x - x)$

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Problem 706

Find the limit: $\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)$ .

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Problem 707

Find the limit: $\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}$ .

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Problem 708

Find the limit $\lim _{x \rightarrow a}\left\{[h(x)]^{2}-f(x) g(x)\right\}$ given $\lim _{x \rightarrow a} f(x)=3$ , $\lim _{x \rightarrow a} g(x)=5$ , $\lim _{x \rightarrow a} h(x)=-2$ .

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Problem 709

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

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Limits & Continuity

Problem 701

Evaluate the limit using L'Hospital's rule $\lim _{x \rightarrow 0} \frac{3^{x}-4^{x}}{x}$

Problem 702

Name: $\qquad$ Part 1. Multiple Choice Graphing Calculator Permitted. Select the correct answer for each problem. Be sure to fill out the answer sheet on the back of the test. (a) $-\frac{9}{2}$ (b) -4 (c) 4 (d) $\frac{9}{2}$

Problem 703

Find the limit: $\lim _{x \rightarrow 1} \frac{x}{\ln x}$ .

Problem 704

Find the limit: $\lim _{x \rightarrow e}(x \ln x - x)$ .

Problem 705

Calculate the limit: $\lim _{x \rightarrow e}(x \ln x - x)$

Problem 706

Find the limit: $\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)$ .

Problem 707

Find the limit: $\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}$ .

Problem 708

Find the limit $\lim _{x \rightarrow a}\left\{[h(x)]^{2}-f(x) g(x)\right\}$ given $\lim _{x \rightarrow a} f(x)=3$ , $\lim _{x \rightarrow a} g(x)=5$ , $\lim _{x \rightarrow a} h(x)=-2$ .

Problem 709

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$

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Limits & Continuity

Problem 701

Evaluate the limit using L'Hospital's rule lim⁡x→03x−4xx\lim _{x \rightarrow 0} \frac{3^{x}-4^{x}}{x}x→0lim​x3x−4x​

Problem 702

Name: \qquad Part 1. Multiple Choice Graphing Calculator Permitted. Select the correct answer for each problem. Be sure to fill out the answer sheet on the back of the test. (a) −92-\frac{9}{2}−29​ (b) -4 (c) 4 (d) 92\frac{9}{2}29​

Problem 703

Find the limit: lim⁡x→1xln⁡x\lim _{x \rightarrow 1} \frac{x}{\ln x}limx→1​lnxx​.

Problem 704

Find the limit: lim⁡x→e(xln⁡x−x)\lim _{x \rightarrow e}(x \ln x - x)limx→e​(xlnx−x).

Problem 705

Calculate the limit: lim⁡x→e(xln⁡x−x)\lim _{x \rightarrow e}(x \ln x - x)limx→e​(xlnx−x)

Problem 706

Find the limit: lim⁡x→0ln⁡(ex+1)\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)limx→0​ln(ex+1).

Problem 707

Find the limit: lim⁡x→∞x+14x2+2\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}limx→∞​4x2+2​x+1​.

Problem 708

Problem 709

lim⁡x→0+x−1−2ln⁡x2x\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}limx→0+​x−1−x​2lnx2​

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Evaluate the limit using L'Hospital's rule $\lim _{x \rightarrow 0} \frac{3^{x}-4^{x}}{x}$

Name: $\qquad$ Part 1. Multiple Choice Graphing Calculator Permitted. Select the correct answer for each problem. Be sure to fill out the answer sheet on the back of the test. (a) $-\frac{9}{2}$ (b) -4 (c) 4 (d) $\frac{9}{2}$

Find the limit: $\lim _{x \rightarrow 1} \frac{x}{\ln x}$ .

Find the limit: $\lim _{x \rightarrow e}(x \ln x - x)$ .

Calculate the limit: $\lim _{x \rightarrow e}(x \ln x - x)$

Find the limit: $\lim _{x \rightarrow 0} \ln \left(e^{x+1}\right)$ .

Find the limit: $\lim _{x \rightarrow \infty} \frac{x+1}{\sqrt{4 x^{2}+2}}$ .

$\lim _{x \rightarrow 0^{+}} x-1-\frac{2 \ln x^{2}}{\sqrt{x}}$