﻿ Let Xn = 1 - 1321 - 1621 - 1102 ... 1 - 1nn + 12, n ≥ 2Then, the value of limn→∞xn is | Limits and Derivatives

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# Limits and Derivatives

#### Multiple Choice Questions

11.

Let f(x) = x13 + x11 + x9 + x7 + x5 + x3 + x + 19. Then , f(x) = 0 has

• 13 real roots

• only one positive and only two negative real roots

• not more than one real root

• has two positive and one negative real root

12.

is equal to

• 1

• does not exist

• $\sqrt{\frac{2}{3}}$

• $\mathrm{ln}\left(2\right)$

13.

The value of  is

# 14.Let Then, the value of $\underset{\mathrm{n}\to \infty }{\mathrm{lim}}{\mathrm{x}}^{\mathrm{n}}$ is1/3 1/9 1/81 0

B.

1/9

We have,

15.

• $\frac{1}{2}$

• $\frac{1}{3}$

• $\frac{2}{3}$

• 0

16.

Let f:  be differentiable at x = 0. If f(0) = 0 and f'(0) = 2, then the value of

is

• 2015

• 0

17.

If  exists and is equal to 1, then the value of $\mathrm{\alpha }$ is

• 2

• 1

• 0

• - 1

18.

Let f(x) be a differentiable function and f'(4) = 5. Then

equals

• 0

• 5

• 20

• - 20

19.

Let [x] denote the greatest integer less than or equal to x for any real number x. Then,

$\underset{\mathrm{n}\to \infty }{\mathrm{lim}}\frac{\left[\mathrm{n}\sqrt{2}\right]}{\mathrm{n}}$ is equal to

• 0

• 2

• $\sqrt{2}$

• 1

20.

The limit of  as

• approaches

• approaches

• is equal to ${\mathrm{log}}_{\mathrm{e}}\left(2013\right)$

• does not exist