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- Unit 02: Differentiation
- one example: We have to find the derivative of $\frac{x+1}{x-1}$ with respect to $x$. ===Method 1=== $$ \begin{aligned} \frac{d}{dx}\left(\frac{x+1}{x-1}\right) &= \frac{(x-1)\frac{d}{dx}(x+1)-(x+1)\frac{d}{dx}(x-1)}{(x-1)^2}\\ &= \frac{(x-1)(1)-(
- Unit 01: Functions and Limits
- imits of Important Functions * $\lim_{x\to a}\frac{x^n-a^n}{x-a} = na^{n-1}$, where n is an integer and a>0 * $\lim_{x\to0}\frac{\sqrt{x+a} - \sqrt{a}}{x} = \frac{1}{2\sqrt{a}}$ * Limit at Infinity * Methods for Evaluating the limits at Infinity * $\lim_{x\to0}(1+\frac{1}{n})^n = e$ * $\lim_{x\to0}\frac{a^x-1}{x}