Limits Theorems
CraigsMaths
Mathematics Teaching for Learning
Engineering Maths B, Limits
October 6th, 2008 by Craig Rose
Permalink: http://www.craigsmaths.com/ea003-engineering-mathematics-b/limits-theorems/
Limits theorems are used to find a limit for function that may be comprised of many terms. Using the theorems split the original function into 2 or more functions and evaluate the limits to each part seperately. Then recombine each individual limit to get the limit of the original function.
Limit theorem 1
The limit of a function will only exist if the function approaches the same value from the left as the right. This will be the case for all continuous functions and only some discontinous functions.
If 
then 
exists.
Limit theorem 2
![\displaystyle\lim_{x \to a}\left[f(x)\pm g(x)\right]= \lim_{x \rightarrow a}f(x) \pm \lim_{x \rightarrow a}g(x)](http://www.craigsmaths.com/wordpress/wp-content/cache/tex_c0a9b31119441254701627d9bc75aca3.png)
Limit theorem 3
![\displaystyle\lim_{x \to a}\left[f(x) \times g(x)\right]= \lim_{x \rightarrow a}f(x) \times \lim_{x \rightarrow a}g(x)](http://www.craigsmaths.com/wordpress/wp-content/cache/tex_faf1eb9ac4715d6dbbfba5be93671d60.png)
Limit theorem 4
![\displaystyle\lim_{x \to a}\left[\frac{f(x)}{g(x)}\right]= \frac{\displaystyle\lim_{x \rightarrow a}f(x)}{\displaystyle\lim_{x \rightarrow a}g(x)}](http://www.craigsmaths.com/wordpress/wp-content/cache/tex_41db0e1c18fb593ec314473c37f11b1f.png)
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