Evaluating limits is sometimes a very tedious job especially when you're really not into it. While it is very helpful for learners to evaluate limits firsthand, it is also useful to just refer to tables for answers to common limits. Plus, it saves time and effort. The following are the tables of common limits which I hope will help us a lot through the course of calculus. There's no need for you to memorize these.
Some ordinary limits
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Simple Functions
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| 1.\lim_{x \to k}a=a | ; a is constant |
| 3.\lim_{x \to k}ax + b=ak + b | ; a and b are constants |
| 4.\lim_{x \to k}x^{r} = k^r | ; r > 0 and an integer |
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Limits involving trigonometric functions
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Simple Trigonometric Functions
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| 1.\lim_{x \to k}\sin{x}=\sin{k} | |
| 2.\lim_{x \to k}\cos{x}=\cos{k} | |
| 3.\lim_{x \to k}\frac{\sin{x}}{x}=1 | |
| 4.\lim_{x \to k}\frac{1-\cos{x}}{x}=0 | |
| 5.\lim_{x \to k}\frac{1-\cos{x}}{x^2}=\frac{1}{2} | |
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Common limits for general functions
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If \lim_{x \to k}f(x)=L_1 and \lim_{x \to k}g(x)=L_2, then
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| 1.\lim_{x \to k}[f(x)\pm g(x)]=L_1\pm L_{2} | |
| 2.\lim_{x \to c}[f(x)\cdot g(x)]=L_1\cdot L_{2} | |
| 3.\lim_{x \to k}\frac{f(x)}{g(x)}=L_1\over L_{2} | ; L\neq 0 |
| 4.\lim_{x \to k}f(x)^{n}=L_{1}^{n} | ; n > 0 |
| 5.\lim_{x \to k}f(x)^{\frac{1}{n}}=L_{1}^{\frac{1}{n}} | ; n > 0, n is even and L_{1} > 0 |
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Limits involving logarithmic and exponential functions
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Simple Functions logarithmic and exponential functions
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| 1.\lim_{x \to 0^+}\log_{b}{x}=-\infty | |
| 2.\lim_{x \to \infty}\log_{b}{x}=\infty | |
| 3.\lim_{x \to -\infty }k^x=0 | ; k is a constant |
| 4.\lim_{x \to \infty }k^x=\infty | ; k is a constant |
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NEXT TABLE: Table of derivatives
