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