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Let lim f(x) = 3 and lim g(x) = 9. Use the limit rules to find the following limit X-3 X-3f(x) + g(x) lim 4g(x) X-3f(x) + lim 4g(x) X-3 (Simplify your answer: Type...

Question

Let lim f(x) = 3 and lim g(x) = 9. Use the limit rules to find the following limit X-3 X-3f(x) + g(x) lim 4g(x) X-3f(x) + lim 4g(x) X-3 (Simplify your answer: Type an integer or a fraction )

Let lim f(x) = 3 and lim g(x) = 9. Use the limit rules to find the following limit X-3 X-3 f(x) + g(x) lim 4g(x) X-3 f(x) + lim 4g(x) X-3 (Simplify your answer: Type an integer or a fraction )



Answers

use algebra to find the limit exactly. $$\lim _{x \rightarrow-3} \frac{x^{2}-9}{x+3}$$

So we need to find the limit of X squared minus three X over x minus three as X approaches three. So notice if you plug three in, you'll get nine minus nine over 3 93. So your kids here over zero, which is an indeterminate form. We need to simplify this function. So this is the limit. Yes. Purchase three. Factor out. An X Makes that X -3, Have X -3 on the bottom, they cancel. So the limit oh, X approaches three of X is equal 23

Limit Acts approaches three of ex choir negative nine upon X negative three. So here in this question we have to find the limit. Use I'll help you to rule if it applies. So here we know that let F of X equal to ex Squire negative nine and G of x equal to X -3. Then you can see that here Acts approaches three. So Up of three equal to three to the power to negative nine. So here we get nine negative nine equal to zero and G of three equal to 3 -3 equal to zero. So here you can see that half of three equal to of three equal to zero. Therefore limit X approaches three of Ex choir 9-9 upon X negative three. Now as X approaches zero sorry three we can perform direct superstition. So here we get zero upon zero and it is indeterminate form. So here we know that very very well. G 03 equal to one. So you can see that here the derivative of G 03 is not equal to zero. So here we can apply al hospital rule. So we know that limit Acts approaches three of ex choir negative nine upon X negative three. So here we have to use all capital rules. So limit Acts approaches three delivery off ap of X upon delivery of G of X. So here you can see that the dairy were you off F of X equal to two time x and their derivative of G of X equal to one. So we put here limit X approaches three off two x upon one. Now as X approaches three we can perform direct substitution. So here we get two times three equal to six. So our limited six it is a war final answer.

Problem Number three ah, limit off extends to three off the function X Q minus three X squared. I lost mine X Simply we can evaluate you think three So three You minor three b squared Last nine 53 is equal to when you step.

Hello. And the project has given that the minutes and a offenses three limit experience for a yes, it was okay to be able to find limited starts today. Price of events, ministries of years, those of effect. So yes, we have inspired this limit from the property. Well, maybe we can buy place of limited stands today affects my stress results live eight experts today. Yes. So that will be her support into three minus three. Well, so that we request to six minus but the very first two months of six. So this is the answer. I hope your sessions. Thanks.


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