## anonymous 3 years ago Limit Help lim as x approches -4 ((1/4)+(1/x)/(4+x)

1. anonymous

Does that make sense or should i draw it?

2. zepdrix

$\huge \lim_{x \rightarrow -4}\frac{\frac{1}{4}+\frac{1}{x}}{4+x}$ It makes sense c: But I wanted to format it anway, heh.

3. anonymous

yes that is it we have only covered limit laws so far.

4. zepdrix

Ok this one isn't too bad.. it's just to test your silly math skills. So first let's get a common denominator on top.

5. anonymous

My "silly" math skills are slowly coming back I took precalc 5 years ago

6. zepdrix

Remember how to get a common denominator? We'll just multiply them both together, that will be the easiest way to do it. So our common denominator will be 4x. It looks like the first term is missing an x, while the second term is missing a 4, So let's fix that. $\huge \lim_{x \rightarrow -4}\frac{\left(\color{cornflowerblue}{\frac{x}{x}}\cdot \frac{1}{4}\right)+\left(\frac{1}{x}\cdot \color{cornflowerblue}{\frac{4}{4}}\right)}{4+x}$Understand that part ok? :D

7. zepdrix

$\huge \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x}$

8. anonymous

okay so now can the denominator of the whole problem cancel out the numerator on the top leaving 4x?

9. zepdrix

oh well, um let's be careful a sec :)

10. zepdrix

We can write our problem like this,$\large \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x} \qquad =\qquad \lim_{x \rightarrow -4} \left(\frac{4+x}{4x}\right)\cdot \frac{1}{4+x}$

11. zepdrix

Maybe this will help you see what's going on better. So what happens when we cancel those out? :O

12. anonymous

it is 1/4x so the lim will be -1/16

13. zepdrix

Yay good job \c:/

14. anonymous

thank you!