MCQs of Continuity and Differentiability | GUJCET MCQ

Continuity and Differentiability MCQs

MCQs of Continuity and Differentiability

Showing 11 to 20 out of 130 Questions

11.

If f (x) = \{\begin{matrix} \frac{x^{2}}{a} - a & x < a \\ 0 & x = a \\ a - \frac{x^{2}}{a} & x > a \end{matrix} then . . .

(a)	$\underset{x \to a +}{l i m} f (x) = a$
(b)	$\underset{x \to a}{l i m} f (x) = - a$
(c)	$f is continuous at x = a$
(d)	$f is differentiable at x = a$

12.

If y = a s i n x + b c o s x, y^{2} + (y_{1})^{2} =_____. (a^{2} + b^{2} \neq 0)

(a)	$a c o s x - b s i n x$
(b)	$(a s i n x - b c o s x)^{2}$
(c)	$a^{2} + b^{2}$
(d)	0

13.

\frac{d}{d x} (x^{2} + s i n^{2} x)^{3} =______.

(a)	$3 (x^{2} + s i n^{2} x)$
(b)	$3 (x^{2} + s i n^{2} x)^{2} (2 x + s i n 2 x)$
(c)	$2 x + 2 s i n x c o s x$
(d)	0

14.

\frac{d}{d x} \sqrt{x s i n x}

= _____ . 0<x<π

(a)	$\frac{x s i n x + c o s x}{\sqrt{x s i n x}}$
(b)	$\frac{x c o s x}{2 \sqrt{x s i n x}}$
(c)	$\frac{x c o s x + s i n x}{2 \sqrt{x s i n x}}$
(d)	$\frac{1}{2 \sqrt{x s i n x}}$

15.

\frac{d}{d x} t a n^{- 1} \frac{1 - x}{1 + x} =_____.

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

16.

\frac{d}{d x} t a n^{- 1} \sqrt{\frac{1 - c o s x}{1 + c o s x}} =_____. π < x < 2 π

(a)	$\frac{1}{1 + c o s^{2} x}$
(b)	$- \frac{1}{1 + c o s^{2} x}$
(c)	$\frac{1}{2}$
(d)	$- \frac{1}{2}$

17.

If x = e^{t a n^{- 1} \frac{y - x^{2}}{x^{2}}}, then \frac{d y}{d x} =_____.

(a)	$2 x (t a n (l o g x) + 1)$
(b)	$2 x (t a n (l o g x) + 1) + x^{2} s e c (l o g x)$
(c)	$(t a n (l o g x) + 1) + x^{2} s e c (l o g x)$
(d)	0

18.

\frac{d}{d x} s i n^{- 1} (\begin{matrix} \frac{3 x}{5} + & \frac{4}{5} \sqrt{1 - x^{2}} \end{matrix}) =_____. (\begin{matrix} 0 < x < & \frac{3}{5} \end{matrix})

(a)	$\frac{3}{5} + \frac{1}{\sqrt{1 - x^{2}}}$
(b)	$\frac{4}{5} \frac{1}{\sqrt{1 - x^{2}}}$
(c)	$- \frac{1}{\sqrt{1 - x^{2}}}$
(d)	$\frac{1}{\sqrt{1 - x^{2}}}$

19.

\frac{d}{d x} t a n^{- 1} (\frac{x + a}{1 - x a}) =_____. (x, a \in R^{+}, x a > 1)

(a)	$\frac{1}{1 + x^{2}}$
(b)	$\frac{1}{1 + a^{2}}$
(c)	$\frac{1}{1 + x^{2}} + \frac{1}{1 + a^{2}}$
(d)	$\frac{1}{1 + x^{2} a^{2}}$

20.

If f(x) = log₇(log₃x), then f'(x) = _____

(a)	$\frac{1}{x l o g 7 l o g 3}$
(b)	$\frac{1}{l o g 3 l o g x}$
(c)	$\frac{1}{x l o g x l o g 7}$
(d)	$\frac{1}{x l o g x}$

Showing 11 to 20 out of 130 Questions