Lecture Eighteen Practice

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Practice problems for Lecture Eighteen Content

1 : Compute the limit $\lim \limits _{x\rightarrow \infty } \frac {\ln (x)}{x^2+1} = \answer {0}$

2 : Compute the limit $\lim \limits _{x\rightarrow \infty } \frac {e^x}{x^2} = \answer {\infty }$

3 : Compute the limit $\lim \limits _{x\rightarrow \infty } \frac {\ln (x)}{\sqrt {x}} = \answer {0}$

4 : Compute the limit $\lim \limits _{x\rightarrow 0} \frac {\tan (x)-x}{x^3} = \answer {\frac {1}{3}}$

5 : Compute the limit $\lim \limits _{x\rightarrow 1} \frac {x^3 - 2x^2 + 1}{x^3 - 1} = \answer {-\frac {1}{3}}$

6 : Compute the limit $\lim \limits _{x\rightarrow \infty } x\sin \left (\frac {\pi }{x}\right ) = \answer {\pi }$

7 : Compute the limit $\lim \limits _{x\rightarrow \infty } \sqrt {x}e^{-\frac {x}{2}} = \answer {0}$

8 : Compute the limit $\lim \limits _{x\rightarrow -\infty } x\ln \left (1-\frac {1}{x}\right ) = \answer {-1}$

9 : Compute the limit $\lim \limits _{x\rightarrow 0^{+}} \left (\frac {1}{x} - \frac {1}{e^x - 1}\right ) = \answer {\frac {1}{2}}$

10 : Compute the limit $\lim \limits _{x\rightarrow 0} \csc (x) - \cot (x) = \answer {0}$

11 : Compute the limit $\lim \limits _{x\rightarrow 0^+} x^{\sqrt {x}} = \answer {1}$

12 : Compute the limit $\lim \limits _{x\rightarrow \infty } \left (1 + \frac {a}{x}\right )^{bx} = \answer {e^{ab}}$

13 : Compute the limit $\lim \limits _{x\rightarrow 1} (2-x)^{\tan (\frac {\pi x}{2})} = \answer {e^{\frac {2}{\pi }}}$

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shift+ctrl+left/right	Add copy of current entry/column to to list/matrix
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shift+ctrl+up/down	Add copy of current row to matrix
ctrl+backspace	Delete current entry in list or column in matrix
ctrl+shift+backspace	Delete current row in matrix

Type...	...to get
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cos	$\cos\left(\blue{[?]}\right)$
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Lambda	$\Lambda$
Xi	$\Xi$
Pi	$\Pi$
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Phi	$\Phi$
Psi	$\Psi$
Omega	$\Omega$

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