New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Limits Continuity and Differentiability question

2011 · Shift 0 · Q30

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Limits Continuity and Differentiability
2011 · Shift 0 · Q30

Limits Continuity and Differentiability question

2011 · Shift 0 · Q30

JEE MainMathematicsLimits Continuity and DifferentiabilityMCQ+4 / −1

The value of

p

and

q

for which the function

f\left( x \right) = \left\{ {\begin{matrix} {{{\sin (p + 1)x + \sin x} \over x}} & {,x \lt 0} \\ q & {,x = 0} \\ {{{\sqrt {x + {x^2}} - \sqrt x } \over {{x^{3/2}}}}} & {,x \gt 0} \\ \end{matrix} } \right.

is continuous for all

x

in R, are

A
$p ={5 \over 2}$ , $q = {1 \over 2}$
B
$p =-{3 \over 2}$ , $q = {1 \over 2}$
C
$p ={1 \over 2}$ , $q = {3 \over 2}$
D
$p ={1 \over 2}$ , $q = -{3 \over 2}$

More from Limits Continuity and Differentiability

$x \to 2 lim (\frac{1 - c o s { 2 ( x - 2 ) }}{x - 2})$ 2011 · MCQ
Let $f : R \to R$ be a positive increasing function with $x \to \infty lim \frac{f ( 3 x )}{f ( x )} = 1$ . Then $x \to \infty lim \frac{f ( 2 x )}{f ( x )} =$ 2010 · MCQ
Let $f (x) = x ∣ x ∣$ and $g (x) = sin x .$ Statement-1: gof is differentiable at $x = 0$ and its derivative is continuous at that point. Statement-2: gof is twice differentiable at $x = 0$ .2009 · MCQ
Let $f (x) = {(x - 1) sin \frac{1}{x - 1} 0 i f x e 1 i f x = 1$ Then which one of the following is true?2008 · MCQ
The function $f : R / {0} \to R$ given by $f (x) = \frac{1}{x} - \frac{2}{e ^{2 x} - 1}$ can be made continuous at $x$ = 0 by defining $f$ (0) as2007 · MCQ
Let $f : R \to R$ be a function defined by $f (x) = min {x + 1, ∣ x ∣ + 1}$ , then which of the following is true?2007 · MCQ
The set of points where $f (x) = \frac{x}{1 + ∣ x ∣}$ is differentiable is2006 · MCQ
Suppose $f (x)$ is differentiable at x = 1 and $h \to 0 lim \frac{1}{h} f (1 + h) = 5$ , then $f^{'} (1)$ equals2005 · MCQ