MHB Limit of Function at x=0: Does Not Exist (DNE)

[josesalazmat]

hello
I have an exercise which says:

Evaluate the following limit. Enter -I if your answer is −∞, enter I if your answer is ∞, and enter DNE if the limit does not exist.

$$ limx→0[(1/(7x)−(1)/((e^(7x))−1)] $$ e power 7x

when I follow the graph for $$1/7x$$ the limit does not exist (goes to infinite for the right and -infinite for the left)it is the same for $$1/(((e^(7x))−1)$$

my answer is DNE but it is wrong

where is a mistake?

Thanks

Jose

 

[MarkFL]

Let:

$$f(x)=\frac{\dfrac{1}{7x}-1}{e^{7x}-1}$$

We see that:

$$\lim_{x\to0^{-}}f(x)=\lim_{x\to0^{+}}f(x)=\infty$$

Technically, this limit does not exist, but given the instructions, I would answer with "I."