Teaching AP DSC School Assistant 2025 Mock Test Series Mathematics Limit and Continuity Discontinuity
Let \(f(x)=\left\{\begin{array}{cc} x^2 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0 & , x=0 \end{array}\right.\)
Then at x = 0
1
f is continuous but not differentiable
2
f and f′ both are continuous
3
f′ is continuous but not differentiable
4
f is continuous but f′ is not continuous