﻿ The limit of xsine1x as x → 0 | Limits and Derivatives

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# Limits and Derivatives

#### Multiple Choice Questions

21.

The limit of

• does not exist

• is equal to $\frac{1}{2}$

• is equal to 0

• is equal to 1

# 22.The limit of $\mathrm{xsin}\left({\mathrm{e}}^{\frac{1}{\mathrm{x}}}\right)$ as is equal to 0 is equal to 1 is equal to $\frac{\mathrm{e}}{2}$ does not exist

A.

is equal to 0

23.

The limits of

• does not exist

• exists and equals to 0

• exists and approaches to

• exists and approaches to

24.

If f(x) = ex(x - 2)2, then

• f is increasing in (- $\infty$, 0) and (2, $\infty$) and decreasing in (0, 2).

• f is increasing in (- ) and decreasing in ()

• f is increasing in (2, $\infty$) and decreasing in (- $\infty$, 0).

• f is increasing in (0, 2) and decreasing in () and (2, $\infty$)

25.

• does not exist

• equals loge(${\mathrm{\pi }}^{2}$)

• equals 1

• lies between 10 and 11

26.

The value of

• 1

• $\frac{1}{{\mathrm{e}}^{2}}$

• $\frac{1}{2\mathrm{e}}$

• $\frac{1}{\mathrm{e}}$

27.

The approximate value of $\sqrt[5]{33}$ correct to 4 decimal places is

• 2.0000

• 2.1001

• 2.0125

• 2.0500

28.

The value of  is

• $\frac{1}{2}{\mathrm{log}}_{\mathrm{e}}\left(1}{2}\right)$

• $\frac{1}{4}{\mathrm{log}}_{\mathrm{e}}\left(1}{2}\right)$

• $\frac{1}{4}{\mathrm{log}}_{\mathrm{e}}\left(2\right)$

• $\frac{1}{2}{\mathrm{log}}_{\mathrm{e}}\left(2\right)$

29.

The value of

• n

30.

$\underset{\mathrm{x}\to 0}{\mathrm{lim}}\frac{\mathrm{sin}\left({\mathrm{\pi sin}}^{2}\left(\mathrm{x}\right)\right)}{{\mathrm{x}}^{2}}$ is equal to

• ${\mathrm{\pi }}^{2}$

• 3$\mathrm{\pi }$

• 2$\mathrm{\pi }$

• $\mathrm{\pi }$