Formulas to calculate Limits

Formulas in NCERT

1. $\lim_{x \to a} \frac{x^n - a^n}{x-a} = n \cdot a^{n-1}$

2. $\lim_{x \to 0} \frac{\sin x}{x} = 1$

3. $\lim_{x \to 0} \frac{1 - \cos x}{x} = 0$

Other Important formulas to calculate limits

4. $\lim_{x \to 0} \frac{\tan x}{x} = 1$

5. $\lim_{x \to 0} \frac{e^x - 1}{x} = 1$

6. $\lim_{x \to 0} \frac{a^x - 1}{x} = \ln a$

7. $\lim_{x \to 0} \frac{\log(1+x)}{x} = 1$

8. $\lim_{x \to \infty} \left(1 + \frac{1}{x}\right)^x = e$

9. $\lim_{x \to 0} (1+x)^{1/x} = e$

10. $\lim_{x \to \infty} \left(1 + \frac{a}{x}\right)^x = e^a$