List of top Mathematics Questions on Continuity and differentiability asked in BITSAT

Let \[ f(x)= \begin{cases} (x-1)\sin\!\left(\dfrac{1}{x-1}\right), & x \neq 1 \\ 0, & x = 1 \end{cases} \] Then which one of the following is true?

If \( x = a \sin \theta \) and \( y = b \cos \theta \), then \( \frac{d^2y}{dx^2} \) is:

Let \( f(x + y) = f(x) \cdot f(y) \) for all \( x, y \), where \( f(0) = 0 \). If \( f(5) = 2 \) and \( f'(0) = 3 \), then \( f'(5) \) is equal to:

The function f(x)=(x-1)√|x| is at x=1:

Let f(x)=(eˣ-1)²(xa)(1+x4) for x≠0, and f(0)=12. If f(x) is continuous at x=0, then the value of a is

Which of the following functions is differentiable at x=0?

Let f(x)=cases ax²+1, & x>1
x+a, & x\le1 cases Then f(x) is derivable at x=1, if