(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find [itex]L=\lim_{x\rightarrow\x_{0}} f(x)[/itex]. Then find a number [itex]\delta > 0[/itex] such that for all x, [itex]0<\left|x-x_{0}\right|<\delta[/itex] [itex]\Rightarrow[/itex] [itex]\left|f(x) - L\right|<\epsilon[/itex]

Problem:

[itex]f(x)=\frac{x^{2}+6x+5}{x+5}[/itex], [itex]x_{0}=-5[/itex], [itex]\epsilon=0.5[/itex]

2. Relevant equations

3. The attempt at a solution

Found the limit first which = -4

[itex]\left|f(x) - L\right|<\epsilon[/itex]

[itex]\left|\frac{x^{2}+6x+5}{x+5} - 4\right|<\epsilon[/itex] <--- Problem here not sure... My teacher seems to sometimes keep the negative limit or sometimes he'll make it positive

[itex]\left|\frac{(x+5)(x+1)}{x+5} - 4\right|<.05[/itex]

[itex]\left|x+1-4\right|<.05[/itex]

[itex]\left|x-3\right|<.05[/itex]

[itex]-.05<x-3<.05[/itex]

[itex]7.95<x+5<8.05[/itex]

[itex]\delta=.05[/itex]

Is that right :|

PS: can someone tell me how to fix the limit in latex?

Thanks.

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# Delta/Epsilon Limit Proof

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