Consider the graphs of f(x), g(x), and their tangent lines at x = 4 shown below (not drawn to scale). The tangent line to f(x) is y = 1.2(x − 4) and the tangent line to g(x) is y = -0.7(x − 4). Find the limit of f(x)/g(x) as x approaches a.

Question

anonymous · Answer

attachment

anonymous · Answer

Find the $$\lim_{x \rightarrow a} \frac{ f(x) }{ g(x) }$$

anonymous · Answer

what is $a$ ? ?

anonymous · Answer

The point of intersection. Its just a random value on the image above that is positive.

anonymous · Answer

$a$ cannot be some "random value" as 
$$\lim_{x\to a}\frac{f(x)}{g(x)}$$ depends on $a$

anonymous · Answer

maybe it is possible that $a=4$?

anonymous · Answer

if so then perhaps this is a l'hopital problem
you want 
$$\lim_{x\to 4}\frac{f(x)}{g(x)}$$  then if you use l'hopital once you get 
$$\lim_{x\to 4}\frac{1.2(x-4)}{-.7(x-4)}$$ which is of the form $\frac{0}{0}$ then use it again and get 
$$\frac{1.2}{-.7}$$

anonymous · Answer

actually that was silly, you don't have to "use it again" just cancel!

anonymous · Answer

Oh, okay. I see.

anonymous · Answer

of course this only works if $a=4$ not for some random $a$ which is probably why the question is confusing