$y=\frac{1-\cos 2x+\sin x}{\sin 2x+\cos x}$ then $\frac{dy}{dx}$ at

Important Questions on Limits and Derivatives

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 16

$\underset{x\to 0}{\lim }\left(1+ax\right){}^{\frac{b}{x}}=e^2$, where $a,b\in N$, such that $a+b=3$, then the value of $\left(a, b\right)$ is

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 17

$\underset{x\to 1}{\lim }\left[{\sec }^{-1}\left(\frac{{\lambda }^2}{\mathrm{In}x}-\frac{{\lambda }^2}{x-1}\right)\right]$ exists, then $\lambda$ belongs to 

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 18

Let $f\left(x\right)=\frac{\left(x-1\right)}{\left(2x^2-7x+5\right)}$ then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 1

If $\underset{x\to 0}{\lim }{\left[1+x\ln \left(1+b^2\right)\right]}^{\frac{1}{x}}=2b{\sin }^2\theta , b>0$ and $\theta \in (-\mathrm{\pi },\mathrm{\pi }],$ then the value of $\theta$ is

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 2

If $\underset{x\to \infty }{\lim }\left(\frac{x^2+x+1}{x+1}-ax-b\right)=4$ then

 

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JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 4

 Let   $L=\underset{x\to 0}{\lim }\genfrac{}{}{0.1ex}{}{a-\sqrt{a^2-x^2}-\genfrac{}{}{0.1ex}{}{x^2}{4}}{x^4}$, $a > 0$. If $L$is finite, then

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 5

Let $f\left(x\right)=\frac{1-x\left(1+|1-x|\right)}{|1-x|}\cos \left(\frac{1}{1-x}\right)$ for $x\ne 1$. Then