IIT-JEE Limits Problems and Solutions

The list of the limit questions asked in IIT-JEE main examinations for practice and solutions to learn how to find the limit of any function in different methods.

Find $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{2^x-1}{\sqrt{1+x}-1}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{(1-\cos{2x})(3+\cos{x})}{x\tan{4x}}}$

Find $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize {\Bigg(\dfrac{5x^2+1}{3x^2+1}\Bigg)}^\dfrac{1}{x^2}}$

Evaluate $\displaystyle \lim_{x \,\to\, 0}{\normalsize \dfrac{\sin{(\pi\cos^2{x})}}{x^2}}$

Find $\displaystyle \large \lim_{x \,\to\, \infty}{\normalsize \bigg(\dfrac{x^2+5x+3}{x^2+x+3}\bigg)^x}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 0}{\normalsize \dfrac{x\tan{2x}-2x\tan{x}}{(1-\cos{2x})^2}}$

Find $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize \dfrac{\sqrt{1-\cos{2(x-2)}}}{x-2}}$

Evaluate $\displaystyle \large \lim_{x \,\to\, 2}{\normalsize \dfrac{\sqrt{1-\cos{2(x-2)}}}{x-2}}$

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