Given that:
$\lim_{x\rightarrow 2} ((f(x)-\frac{3}{x-2} - \frac{x}{x^2 - 4})=4$
Find $\lim _{x\rightarrow 2 }f(x)$.
how to solve this limits question
0
$\begingroup$
limits
-
1It seems that some brackets are missing. You can use Mathjax to write fraction. Have a look to this tutorial: http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference – 2017-01-24
1 Answers
0
$\lim_{x\rightarrow 2} (f(x)-\frac{3}{x-2} - \frac{x}{x^2 - 4})=4\\\implies\lim_{x\rightarrow 2} f(x)=4+\lim_{x\rightarrow 2}\frac{3}{x-2}+\lim_{x\rightarrow 2} \frac{x}{x^2-4}\\ \textrm{using L'Ho}\hat{p}\textrm{ital Rule}\\\implies\lim_{x\rightarrow 2}f(x)=4+0+\frac{1}{2}=\frac{9}{2}$