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

NCERT EXERCISE 13.1
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Question 15. \( \lim_{x \to \pi}  \frac{\sin (\pi – x)}{\pi (\pi – x)} \)

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

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

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

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