Question

Limit question. Please help

Answer 1

\[\lim_{x \rightarrow 0} = \frac{ 3^{1/x} - 1 }{ 3^{1/x} +1 }\]

Answer 2

are you allowed to use l'hosptal?

Answer 3

No I unfortunately am not allowed to

Answer 4

ok let me think for a sec then on other ways

Answer 5

Ok thanks

Answer 6

ok and do you know how to differentiate 3^(1/x)?

Answer 7

No I do not

Answer 8

\[x>0 \text{ we have } 3^\frac{1}{x}-1>0 \\ x<0 \text{ we have } 3^\frac{1}{x}-1<0 \\ \text{ for any real } x \neq 0 \text{ we have } 3^\frac{1}{x}+1>0 \]

Answer 9

This should help you to conclude something about the actual limit since this giving you information about the left and right limit.

Answer 10

Like we don't need to know the exact left and right limit just that they differ.

Answer 11

For this question I have to show all the work. How would I show that?

Answer 12

Well I know 3^a is positive for any real a
so 3^a+1 is still greater than 0

Answer 13

3^a-1
if a=0 then we have 1-1
but if a<0 then 0<3^a<1 so 3^a-1 will be negative
but if a>0 then 3^a>1 so 3^a-1 will be positive

Answer 14

since the left and right limit differ
then the actual limit doesn't exist

Answer 15

Okay thanks