Let f: R → R be defined as: f(x)= (a-b cos 2 x)/(x²); x 1 If f is continuous everywhere in R and m is the number of points where f is NOT differential then m+a+b+c equals:

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 1 Feb, Morning shift · Q4216

JEE Main 20241 Feb, Morning shiftMathematicsHardLimit, Continuity and Differentiability420× since 2002

Let

f: \mathbf{R} \rightarrow \mathbf{R}

be defined as :

f(x)= \begin{cases}\frac{a-b \cos 2 x}{x^2} ; & x<0 \\\\ x^2+c x+2 ; & 0 \leq x \leq 1 \\\\ 2 x+1 ; & x>1\end{cases}

f

is continuous everywhere in

\mathbf{R}

and

m

is the number of points where

f

is NOT differential then

\mathrm{m}+\mathrm{a}+\mathrm{b}+\mathrm{c}

equals :