Algebraic Limits
| \lim_{x \to a} \frac{x^n-a^n}{x - a} =na^{n-1}, n\ \epsilon\ Q |
| \lim_{x \to 0} \frac{(1+x)^n-1}{x} =n, n\ \epsilon\ Q |
Trigonometric Limits
| \lim_{x \to 0} \frac{sinx}{x} =1= \lim_{x \to 0} \frac{x}{sinx} |
| \lim_{x \to 0} \frac{tanx}{x} =1= \lim_{x \to 0} \frac{x}{tanx} |
| \lim_{x \to 0} \frac{sin^{-1}x}{x} =1= \lim_{x \to 0} \frac{x}{sin^{-1}x} |
| \lim_{x \to 0} \frac{tan^{-1}x}{x} =1= \lim_{x \to 0} \frac{x}{tan^{-1}x} |
Exponential Limits
| \lim_{x \to 0} \frac{e^x-1}{x} =1 |
| \lim_{x \to 0} \frac{a^x-1}{x} =log_ea |
Logarithmic Limits
| \lim_{x \to 0} \frac{log_e(1+x)}{x} =1 |
| \lim_{x \to e}{log_ex} =1 |
| \lim_{x \to 0} \frac{log_e(1-x)}{x} =-1 |
| \lim_{x \to 0} \frac{log_a(1+x)}{x} =log_ae |
Particular Cases
| \lim_{x \to 0} {(1+x)}^{1\over x} =e |
| \lim_{x \to 0} {(1+{1\over x})}^{x} =e |
