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

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# 11.Let f(x) = x13 + x11 + x9 + x7 + x5 + x3 + x + 19. Then , f(x) = 0 has13 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

C.

not more than one real root

f(x) = x13 + x11 + x9 + x7 + x5 + x3 + x + 19

$\therefore$ f'(x) has no real root.

$\therefore$ f'(x) = 0 has not more than one 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 $\underset{\mathrm{n}\to \infty }{\mathrm{lim}}{\mathrm{x}}^{\mathrm{n}}$ is

• 1/3

• 1/9

• 1/81

• 0

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