GATE EC Calculus questions

Practise Calculus questions for GATE EC. Explore official PYQs and original topic-wise quizzes, check answers and view available solutions. Free, no sign-in.

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SubjectTopicYearType

\displaystyle{}\lim _{\theta \rightarrow 0} \frac{\sin (\theta / 2)}{\theta}

Which one of the following functions is strictly bounded?

For the function

e^{-x}

, the linear approximation around

x=2

Consider the function

f(x)=x^{2}-x-2

. The maximum value of

f(x)

in the closed interval

[-4,4]

The integral

\displaystyle{}\int_0^\pi \sin ^3 \theta\; d \theta

is given by

x

is increased from

-\infty

\infty

, the function

f(x)=\frac{e^x}{1+e^x}

f(t)=\frac{\omega}{s^2+\omega^2}

, then the value of

\lim _{t \rightarrow \infty} f(t)

\lim _{x \rightarrow 0} \frac{x\left(e^{x}-1\right)+2(\cos x-1)}{x(1-\cos x)}