When a function is called derivable $?$

Important Questions on Continuity and Differentiability

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\sin x$ derivable $?$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\cos x$ derivable $?$

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\tan x$ derivable $?$

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\cot x$ derivable $?$

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\sec x$ derivable $?$

MEDIUM

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Is the function $f\left(x\right)=\mathrm{cosec} x$ derivable $?$

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

Examine the function $f\left(x\right)=\left\{\begin{array}{ll}1+x , if& x\le 2\\ 5-x , if& x>2\end{array}\right.$ for differentiability at $x=2$.

EASY

12th ICSE

IMPORTANT

Understanding ISC Mathematics Class 12 Volume 1>Chapter 5 - Continuity and Differentiability>EXERCISE 5.4

If $f\left(2\right)=4$ and $f\text{'}\left(2\right)=4$, then evaluate $\underset{x\to 2}{\lim }\frac{x f\left(2\right)-2 f\left(x\right)}{x-2}$.