Question 1 :
What is $\displaystyle \lim _{ x\rightarrow 0 }{ \cfrac { \sqrt { 1+x } -1 }{ x } } $ equal to?
Question 2 :
Let $f(x + y) = f(x) \times f(y)$ for all $x$ and $y$ and $f(7) = 5, f'(0) = 2$ then $f'(7)$ will be
Question 4 :
Obtain the differential equation whose solution is<div>$\displaystyle y=x\sin \left ( x+A \right ),$ A being constant.</div>
Question 9 :
Identify the value of $\displaystyle\lim_{x \rightarrow 2} x^2 - 5x + 6$
Question 10 :
If $f ( x ) = \dfrac { a ^ { x } } { x ^ { a } }$ then $f ^ { \prime } ( a ) =$
Question 14 :
$\displaystyle \frac{d}{dx}\left ( \tan ^{-1}\left ( \frac{a-x}{1+ax} \right ) \right )$ equals if ax > -1
Question 15 :
$\underset { x\rightarrow 0 }{ \lim } { \left( 1+\dfrac { 2 }{ { x }^{ 2 } } \right) }^{ { x }^{ 2 } }=$
Question 17 :
Differentiate with respect to x $\displaystyle \frac{\left ( 1+x \right )}{e^{x}}$<br/>
Question 19 :
If function $f(x)=\cfrac{{x}^{3}-{a}^{3}}{x-a}$, is continuous at $x=a$ then the value of $f(a)$ is-
Question 26 :
The value of $\displaystyle \lim_{x\rightarrow 2}\int_{2}^{x} \dfrac {3t^{2}}{x - 2}dt$ is
Question 27 :
Derivative of $2\tan x - 7\sec x$ with respect to $x$ is:<br/>
Question 28 :
$\displaystyle \frac{d}{dx}[f(x)\cdot g(x)] =f(x) \frac{d}{dx}g(x)+g(x) \frac{d}{dx}f(x)$ is known as _____ rule.
Question 31 :
If $f(x) = x^{2} - 6x + 8$ and there exists a point $c$ in the interval $[2, 4]$ such that $f'(c)=0,$ then what is the value of $c$ ?
Question 32 :
Consider the differential equation $\frac { d y } { d x } = \cos x$ Then we observe that <br/>
Question 33 :
$\mathop {\lim }\limits_{x \to \infty } \sum\limits_{r = 1}^n {{{\tan }^{ - 1}}} \left( {\frac{{2r}}{{1 - {r^2} + {r^4}}}} \right)$ is equal to
Question 35 :
$\underset { x\rightarrow 1 }{ Lt } { (1+\sin\pi x) }{ \pi x }$
Question 36 :
$If\space f(x+y) = f(x) + f(y) +2xy - 6 for\space all\space x,y\space in\space R\space and\space f '(0)=2\space then\space y = f(x)\space will\space be$	<br/>
Question 38 :
What is $\displaystyle \lim_{x \rightarrow -2 } \begin{pmatrix} \dfrac{x+2}{x^3 + 8} \end{pmatrix} $ equal to ?
Question 39 :
$\lim _ { x \rightarrow 0 } \frac { 3 ^ { x } - 2 ^ { x } } { 4 ^ { x } - 3 ^ { x } }$ is equal to
Question 40 :
If $\displaystyle f\left ( x \right )=\left ( \frac{\sin ^{m}x}{\sin ^{n}x} \right )^{m+n}.\left ( \frac{\sin ^{n}x}{\sin ^{p}x} \right )^{n+p}.\left ( \frac{\sin ^{p}x}{\sin ^{m}x} \right )^{p+m}$ then $\displaystyle f'\left ( x \right )$ is equal to-
Question 41 :
Find the value of $\lim_{x \rightarrow 0} \dfrac{2x^2 + 3x + 4}{2}$
Question 44 :
If $\displaystyle y=\frac{1}{\sqrt{\left ( x^{2}+a^{2} \right )}+\sqrt{\left ( x^{2}+b^{2} \right )}},$ find $\displaystyle \frac{dy}{dx}.$
Question 46 :
Find $\dfrac{{dy}}{{dx}}$ of the following $y = 1 + 2x + 3{x^2} + \left( {n - 1} \right){x^{n - 2}}$<br/><br/>
Question 48 :
Find the differential equations of all parabolas each having latus rectum $4a$ and whose axes are parallel to the x-axis.