$\underset{x\to 0^{+}}{\lim }\left(\left(x\cot x\right)+\left(x\log x\right)\right)$ equals

Important Questions on Limits and Derivatives

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 10

$m, n\in I^{+}$, then $\underset{x\to 0}{\lim }\frac{\sin x^n}{(\sin x{)}^m}$ equals

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 11

$\underset{x\to \infty }{\lim }\frac{\left(1+x+x^2\right)}{(\ln x{)}^3}$ is equal to

MEDIUM

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 12

$\underset{x\to 0}{\lim }{\left(\frac{4^x+9^x}{2}\right)}^{\frac{1}{x}}$ equals

EASY

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 13

If $\underset{x\to \infty }{\lim }{\left(1+\frac{a}{x}+\frac{b}{x^2}\right)}^{2x}=e^2,$ then the values of $a$ and $b$ are

HARD

JEE Main/Advance

IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 15 - Limits and Derivatives>Assignment>Q 14

If $\alpha$ and $\beta$ be the roots of $a{x}^2+bx+c=0$ , then $\underset{x\to \alpha }{\lim }{\left(1+a{x}^2+bx+c\right)}^{\frac{1}{\left(x-\alpha \right)}}$ is

MEDIUM

JEE Main/Advance

IMPORTANT

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

If $\underset{x\to 0}{\lim }(\cos x+a\sin bx{)}^{1/x}=e^2$, then the values of $a$ and $b$ are

EASY

JEE Main/Advance

IMPORTANT

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

Let $f\left(2\right)=4,f^{\text{'}}\left(2\right)=4$. Then $\underset{x\to 2}{\lim }\frac{xf\left(2\right)-2f\left(x\right)}{x-2}$ is

EASY

JEE Main/Advance

IMPORTANT

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

If $f\left(4\right)=4, f^{\text{'}}\left(4\right)=1$ then $\underset{x\to 4}{\lim }\frac{2-\sqrt{f\left(x\right)}}{2-\sqrt{x}}$ is equal to