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

The number of points at which the function f(x)=(1)/(log|x|) is discontinuous is

If f(x)= begincases (xlog(cos x))/(log(1+x²)), & x≠0
0, & x=0 endcases then f(x) is

If
\[ f(x) = \frac{x}{1+x} + \frac{x}{(x+1)(2x+1)} + \frac{x}{(2x+1)(3x+1)} + \cdots \]

then at \(x = 0\), \(f(x)\) is:

If
\( f(x) = \begin{cases} 1, & 0 < x \le \dfrac{3\pi}{4} \\ 2\sin\left(\dfrac{2x}{9}\right), & \dfrac{3\pi}{4} < x < \pi \end{cases} \)
then:

If f(x)= begincases sin x, & when x is rational
cos x, & when x is irrational endcases then the function is:

If
\[ f(x) = \begin{cases} \dfrac{x \log(\cos x)}{\log(1 + x^2)}, & x \ne 0 \\[2mm] 0, & x = 0 \end{cases} \]
then \(f(x)\) is

Let \(f:\mathbb R\to\mathbb R\) be a function such that \(f(x+y)=f(x)+f(y)\) for all \(x,y\in\mathbb R\). If \(f(x)\) is differentiable at \(x=0\), then which one of the following is incorrect?

If \(y=\left(x+\sqrt{1+x^2}\right)^n\), then \((1+x^2)\dfrac{d^2y}{dx^2}+x\dfrac{dy}{dx}\) is

If a function \(f(x)\) is given by \[ f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2x+1)}+\frac{x}{(2x+1)(3x+1)}+\cdots+\infty, \] then at \(x=0\), \(f(x)\)

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