Limits, Continuity and Differentiability · Mathematics · KCET

If $$\lim _\limits{x \rightarrow 0} \frac{\sin (2+x)-\sin (2-x)}{x}=A \cos B$$, then the values of $$A$$ and $$B$$ respectively are

The function $$f(x)=\cot x$$ is discontinuous on every point of the set

If $$f(x)=\left\{\begin{array}{cc}x^2-1, & 0 the quadratic equation whose roots are $$\lim _\limits{x \rightarrow 2^{-}} f(x)$$ and $$\lim _\limits{x ...

$$\lim _\limits{y \rightarrow 0} \frac{\sqrt{3+y^3}-\sqrt{3}}{y^3}=$$

Consider the following statements statement 1: $$\lim _\limits{x \rightarrow 1} \frac{a x^2+b x+c}{x^2+b x+a}$$ is 1 (where $$a+b+c \neq 0$$). stateme...

If $$f(x)=\left|\begin{array}{ccc}\cos x & 1 & 0 \\ 0 & 2 \cos x & 3 \\ 0 & 1 & 2 \cos x\end{array}\right|$$, then $$\lim _\limits{x \rightarrow \pi} ...

At $$x=1$$, the function $$f(x)=\left\{\begin{array}{cc} x^3-1, & 1...

The right hand and left hand limit of the function are respectively. $$f(x)=\left\{\begin{array}{cc} \frac{e^{1 / x}-1}{e^{1 / x}+1}, & \text { if } x...

$$\lim _\limits{x \rightarrow 0}\left(\frac{\tan x}{\sqrt{2 x+4}-2}\right) \text { is equal to }$$

If $$f(x)=\left\{\begin{array}{cc}\frac{1-\cos K x}{x \sin x}, & \text { if } x \neq 0 \\ \frac{1}{2}, & \text { if } x=0\end{array}\right.$$ is conti...

If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuous at $$x=0$$, then $$k=$$...

$$\sum_\limits{r=1}^n(2 r-1)=x$$ then, $$ \lim _\limits{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac{3^3}{x^2}+\ldots+\frac{n^3}{x...

Rolle's theorem is not applicable in which one of the following cases?