If $f\left(x\right)=\left\{\begin{array}{ccc}\frac{1}{e^{1/x}+1}& ,& x\ne 0\\ 0& ,& x=0\end{array}\right.$, then

Important Questions on Continuity and Differentiability

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 3

If function $f\left(x\right)=\frac{\sqrt{1+x}-\sqrt[3]{1+x}}{x}$, is continuous function, then $f\left(0\right)$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 4

If $f\left(x\right)=\frac{x^2-\left(a+2\right)x+a}{x-2}, \mathrm{for} x\ne 2$ and $f\left(2\right)=2$ is continuous at $x=2$, then $a$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 5

If $f\left(x\right)=\left\{\begin{array}{ccc}\frac{\log \left(1+2ax\right)-\log \left(1-bx\right)}{x}& ,& x\ne 0\\ h& ,& x=0\end{array}\right.$, is continuous at $x=0$, then $k$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 6

If $f\left(x\right)=\left\{\begin{array}{ccc}\left[x\right]+\left[-x\right]& ,& x\ne 2\\ \lambda & ,& x=2\end{array}\right.$, $f$ is continuous at $x=2$ then $\lambda$ is (where $\left[·\right]$ denotes greatest integer)

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 7

If $f\left(x\right)=\left\{\begin{array}{ccc}\frac{1-\cos 4x}{x^2}& ,& x<0\\ a& ,& x=0\\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}-4}}& ,& x>0\end{array}\right.$, then correct statement is-

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 8

A function $f\left(x\right)=\frac{1}{\log \left|x\right|}$ is discontinuous at -

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 9

If $f\left(x\right)=\frac{1-\tan x}{4x-\pi }, x\ne \frac{\pi }{4}, x\in \left[0,\frac{\pi }{2}\right)$ is a continuous function, then $f\left(\frac{\pi }{4}\right)$ is equal to

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Beta Question Bank for Engineering: Mathematics>Chapter 27 - Continuity and Differentiability>EXERCISE-1>Q 10

The value of $f\left(0\right)$, so that the function $f\left(x\right)=\frac{\sqrt{a^2-ax+x^2}-\sqrt{a^2+ax+x^2}}{\sqrt{a+x}-\sqrt{a-x}}$ becomes continuous for all $x$, is given by