JEE Main 2026 (Online) 23rd January Evening ShiftQuestion 1
If $f(x)=\begin{cases}\dfrac{a|x|+x^2-2(\sin|x|)(\cos|x|)}{x}, & x\ne0\\ b, & x=0\end{cases}$ is continuous at $x=0$, then $a+b$ is equal to :
Limits & Continuity
Solution
For $x>0$: limit $=a-2$. For $x<0$: $|x|=-x$, limit $=-a+2$. Continuity: $a-2=2-a=b\Rightarrow a=2,b=0$, so $a+b=2$.