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Revision of basic identities in limits
Some extra and important questions of limits from my assignment

 NCERT EXERCISE 13.1

Question 15. $$\lim_{x \to \pi} \frac{\sin (\pi – x)}{\pi (\pi – x)}$$

Question 22. $$\lim_{x \to \frac{\pi}{2}} \frac{\tan 2x}{x – \frac{\pi}{2}}$$

Some extra and important questions of limits from my assignment
Limits of exponential and logarithmic functions

 SUPPLEMENTARY EXERCISE 13.3

Evaluate the following limits, if exist

Question 1. $$\lim_{x \to 0} \frac{e^{4x}-1}{x}$$

Question 2. $$\lim_{x \to 0} \frac{e^{2+x}-e^2}{x}$$

Question 3. $$\lim_{x \to 5} \frac{e^x-e^5}{x-5}$$

Question 4. $$\lim_{x \to 0} \frac{e^{\sin x}-1}{x}$$

Question 5. $$\lim_{x \to 3} \frac{e^x-e^3}{x-3}$$

Question 6. $$\lim_{x \to 0} \frac{x(e^x-1)}{1- \cos x}$$

Question 7. $$\lim_{x \to 0} \frac{\log_e(1+2x)}{x}$$

Question 8. $$\lim_{x \to 0} \frac{\log (1+x^3)}{\sin^3 x}$$