MCQs of Continuity and Differentiability

Showing 31 to 40 out of 117 Questions

31.

\frac{d}{d x} \frac{1}{\log |x|} =_____.

32.

f (x) = \frac{1 - \cos 2 x}{x^{2}}, x \neq 0 = k, x = 0 If f is continuous at x = 0, then k =

33.

f (x) = \{\begin{cases} \frac{x^{n} - 1 - n (x - 1)}{(x - 1)^{2}}, x \neq 1 \\ \frac{n (n - 1)}{2}, x = 1 \end{cases} If f is continuous at x = 1, then \lim_{x \to 1} \frac{x^{n} - 1 - n (x - 1)}{(x - 1)^{2}} =

34.

If f (x) = \sin |x|, then

_____

(a)	f is continuous for all $x \in R$
(b)	f is continuous for some $x \in R$
(c)	f is differential for all $x \in R$
(d)	none of these

35.

If f (x) = \frac{\tan (π [x - π])}{1 + {[x]}^{2}}, then . .

(a)	f is continuous for some $x \in R$
(b)	$\forall x \in R, f is continuous but f' (x) does not exist$
(c)	$\forall x \in R f' (x) exists$
(d)	$\forall x \in R f' (x) exists but f'' (x) does not exist$

36.

f (x) = [\sin x] is . . . . a t x = \frac{π}{2}

37.

If f is even function and f' (2) = 5, then f' (- 2) =

_____

38.

If f (x) = |\cos x|, t h e n . f' (\frac{5 π}{6}) =

_____

w h e r e \frac{π}{2} < x < π

39.

If f (x) = |x - 2| and g = f o f, then g' (x) =

_____

; 2 < x < 4

40.

If f (x) = 3 |2 + x|, then f' (- 3) =

_____

Showing 31 to 40 out of 117 Questions