For $\underset{x\to 0}{\mathrm{Lim}}\frac{{\cot }^{-1}\left(\frac{1}{x}\right)}{x}$

Important Questions on Limits

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 23

If $\ell =\underset{x\to \infty }{\lim }{\left(\frac{x+1}{x-1}\right)}^x$, then $\left\{\ell \right\}$ and $\left[\ell \right]$ (where $\left\{.\right\}$ & $\left[.\right]$ denotes the fractional part function & greatest integer function respectively), is/are -

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 24

Which of the following limits is/are unity?

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 25

If $f\left(x\right)=\left\{\begin{array}{ll}\frac{\sin \left[x\right]}{\left[x\right]},& \left[x\right]\ne 0\\ 0,& \left[x\right]=0\end{array}\right.$ where $\left[x\right]$ denotes the greatest integer less than or equal to $x$, then

MEDIUM

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 26

Which of the following limits vanishes?

HARD

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Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 27

${Lim}_{x\to 0^{+}}\left(\left(x^{x^x}\right)-x^x\right)$

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 28

Let $\ell ={Lim}_{x\to 0}{x}^m(\ell nx{)}^n$ where $m,n\in N$ then -

EASY

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 30

If $g\left(x\right)$ is a polynomial satisfying $g\left(x\right) g\left(y\right)=g\left(x\right)+g\left(y\right)+g\left(xy\right)-2$ for all real $x$ and $y$ and $g\left(2\right)=5$ then $g\left(3\right)$ is equal to-

HARD

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IMPORTANT

Beta Question Bank for Engineering: Mathematics>Chapter 26 - Limits>EXERCISE-2>Q 31

Let $n$ be an odd integer. If $\sin n\theta =\sum _{r=0}^n{b}_r{\sin }^r\theta$, for every value of $\theta$, then -