Limits and Derivatives Lecture 3
Play Video

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}