If $8f\left(x\right)+6f\left(\frac{1}{x}\right)=x+5$ and $y=x^{2}f\left(x\right)$, then $\frac{dy}{dx}$ at $x=-1$ is equal to

Important Questions on Introduction to Limits and Derivatives

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Target Exercises>Q 121

If $f\left(x\right)=\log \left|2x\right|, x\ne 0$, then $f^{\text{'}}\left(x\right)$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Target Exercises>Q 122

If $f\left(x\right)=\left|x-3\right|$ and $\varphi \left(x\right)=\left(fof\right)\left(x\right),$ when $x>10$. Then, ${\varphi }^{\text{'}}\left(x\right)$ is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Target Exercises>Q 123

If $f\left(x\right)$ is a polynomial of degree $n\left(>2\right)$ and $f\left(x\right)=f\left(k-x\right),$ where $k$ is a fixed real number. Then, the degree of $f^{\text{'}}\left(x\right)$ is

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Entrances Gallery>Q 7

$\underset{x\to 0}{\lim }\frac{\left(1-\cos 2x\right)\left(3+\cos x\right)}{x\tan 4x}$ is equal to

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Entrances Gallery>Q 8

If the function $g\left(x\right)=\left\{\begin{array}{ll}k\sqrt{x+1}& ,0\le x\le 3\\ mx+2& ,3<x\le 5\end{array}\right.$ is differentiable, then the value of $k+m$ is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Entrances Gallery>Q 9

Let $f\left(x\right)$ be a polynomial of degree four having extreme values at $x=1$ and $x=2.$ If $\underset{x\to 0}{\lim }\left[1+\frac{f\left(x\right)}{x^2}\right]=3$ then $f\left(2\right)$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Entrances Gallery>Q 10

$\underset{x\to 0}{\lim }\frac{\sin \left(\pi {\cos }^{2}x\right)}{x^2}$ is equal to

EASY

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 18 - Introduction to Limits and Derivatives>Entrances Gallery>Q 11

$\underset{x\to 0}{\lim }\frac{\left(1-\cos 2x\right)\left(3+\cos x\right)}{x\tan 4x}$ is equal to