MCQs of Continuity and Differentiability | GUJCET MCQ

Continuity and Differentiability MCQs

MCQs of Continuity and Differentiability

Showing 1 to 10 out of 130 Questions

1.

{[\frac{d}{d x} s e c^{- 1} x]}_{x = - 3} =

(a)	$\frac{1}{\sqrt{x^{2} - 1}}$
(b)	$- \frac{1}{\sqrt{x^{2} - 1}}$
(c)	$\frac{1}{6 \sqrt{2}}$
(d)	$\frac{- 1}{6 \sqrt{2}}$

2.

\frac{d}{d x} x^{x} =_____(x > 0)

(a)	$x^{x - 1}$
(b)	$x^{x}$
(c)	0
(d)	$x^{x} (1 + l o g x)$

3.

\frac{d}{d x} (s i n^{- 1} x + c o s^{- 1} x) =_____(|x| < 1)

(a)	0
(b)	$\frac{2}{\sqrt{1 - x^{2}}}$
(c)	$\frac{1}{\sqrt{1 - x^{2}}}$
(d)	$does not exist$

4.

\frac{d}{d x} a^{a} =_____(a > 0)

(a)	$a^{a} (1 + l o g a)$
(b)	0
(c)	$a^{a}$
(d)	$does not exist$

5.

\frac{d}{d x} e^{5 x} =_____.

(a)	$e^{5 x}$
(b)	$5 e^{5 x}$
(c)	$5 x e^{5 x - 1}$
(d)	0

6.

\frac{d}{d x} l o g |x| =_____. (x \neq 0)

(a)	$\frac{1}{\|x\|}$
(b)	$\frac{1}{x}$
(c)	$does not exist$
(d)	$e^{x}$

7.

\frac{d}{d x} s i n^{3} x =_____.

(a)	$3 s i n^{2} x$
(b)	$3 c o s^{2} x$
(c)	$3 s i n^{2} x c o s x$
(d)	$- 3 c o s^{2} x s i n x$

8.

\frac{d}{d x} t a n^{n} x =____.

(a)	$n t a n^{n - 1} x$
(b)	$n t a n^{n - 1} x s e c^{2} x$
(c)	$n s e c^{2 n} x$
(d)	$n t a n^{n - 1} x s e c^{n - 1} x$

9.

If f (x) = \{\begin{cases} x x \in (0, 1) \\ 1 x \geq 1 \end{cases}

(a)	$f is continuous at x = 1 only$
(b)	$f is discontinuous at x = 1 only$
(c)	$f is continuous on R^{+}$
(d)	$f is not defined for x = 1$

10.

I f f (x) = \{\begin{matrix} a x + b & 1 \leq x < 5 \\ 7 x - 5 & 5 \leq x < 10 \\ b x + 3 a & x \geq 10 \end{matrix} i s c o n t i n u o u s, (a, b) =_____.

(a)	(5, 10)
(b)	(5, 5)
(c)	(10, 5)
(d)	(0, 0)

Showing 1 to 10 out of 130 Questions