MHB 3.4.238 AP calculus exam Limits with ln

[karush]

238
Solve
$$\displaystyle\lim_{h\to 0}
\dfrac{\ln{(4+h)}-\ln{h}}{h}$$
$$(A)\,0\quad
(B)\, \dfrac{1}{4}\quad
(C)\, 1\quad
(D)\, e\quad
(E)\, DNE$$
The Limit diverges so the Limit Does Not Exist (E)ok the only way I saw that it diverges is by plotting
not sure what the rule is that observation would make ploting not needed

also I noticed these AP sample questions are getting a lot of views so thot I would continue to post more

 

[skeeter]

Check your limit expression again. Should be

$\displaystyle \lim_{h \to 0} \dfrac{\ln(4+h) - \color{red}{ \ln(4)}}{h}$
Recall the limit definition of a derivative ...

$\displaystyle f’(x) = \lim_{h \to 0} \dfrac{f(x+h)-f(x)}{h}$

let $x=4$

... try again.