Security Is Mostly A Superstition. Life Is Either A Daring Adventure Or Nothing. – Helen Keller

# Lecture - 3 Chapter 13 Limits and Derivatives

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

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