﻿ If y = tan-11 - sinx1 + sinx, then the value of dydx at x = π6 is | Limits and Derivatives

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# Limits and Derivatives

31.

If N = n!(n , then find

32.

Use the formula

#### Multiple Choice Questions

33.

The value of

• 1

• $\frac{1}{2}$

• 0

34.

The value of

• e2

• e

• $\frac{1}{\mathrm{e}}$

• $\frac{1}{{\mathrm{e}}^{2}}$

35.

If f(5)=7 and f'(5)=7 then  is given by

• 35

• - 35

• 28

• - 28

36.

The value of f(0) so that the function  is continuous everywhere is

• $\frac{1}{2}$

• $\frac{1}{4}$

• $\frac{1}{6}$

• $\frac{1}{8}$

37.

$\underset{\mathrm{x}\to 0}{\mathrm{lim}}\frac{\mathrm{sin}\left|\mathrm{x}\right|}{\mathrm{x}}$ is equal to

• 1

• 0

• positive infinity

• does not exist

# 38.If y = , then the value of $\frac{\mathrm{dy}}{\mathrm{dx}}$ at x = $\frac{\mathrm{\pi }}{6}$ is- $\frac{1}{2}$ $\frac{1}{2}$ 1 - 1

A.

$\frac{1}{2}$

39.

The value of the limit

• 0

• e

• $\frac{1}{\mathrm{e}}$

• 1

40.

Let f(x) = , then the value of  is

• 0

• does not exist

• $\frac{1}{2}$