The limit
lim (5^(x)-1)/x
x-0

represents the derivative of some function f(x) at some number a. Find f and a.

Question

The limit 
lim     (5^(x)-1)/x
x->0

represents the derivative of some function f(x) at some number a. Find f and a.

anonymous · Answer

$$\lim_{x \rightarrow 0}5^{x-1} \div x?$$

turingtest · Answer

l'hospital's rule

anonymous · Answer

or$$\lim_{x \rightarrow 0}5^{x}-1 \div x$$?

anonymous · Answer

second one

turingtest · Answer

$$\lim_{x\to0}{5^x-1\over x}$$

anonymous · Answer

yup @TuringTest

turingtest · Answer

use l'Hospital if you are allowed to; take the derivative of the top and bottom, then take the limit again

anonymous · Answer

well im not allowed to use l'hoapital rule

turingtest · Answer

hm....

anonymous · Answer

|dw:1340305376609:dw|
then u will get indeterminant of the form 0/0
you apply L'HOSPITALS RULE

turingtest · Answer

@msamido the asker just stated that we cannot use l'Hospital here, so we must find another way

anonymous · Answer

...but i was thinking that ....it is indeterminant of the form 0/0  ...

turingtest · Answer

yeah$${5^0-1\over0}=\frac00$$and l'Hospital $does$ work, but apparently it's not allowed :(

zarkon · Answer

are you allowed to use one of the definitions of $e$

$$\lim_{x\to0}{e^x-1\over x}=1$$