Question

Evaluate the limit as x approaches infinity.

Answer 1

\[\lim_{x \rightarrow -infinity} \frac{ 6 }{ e^x+7 }\]

Answer 2

do you know \(\displaystyle\lim_{x\to-\infty}e^x\) ?

Answer 3

@Zarkon , I am not sure

Answer 4

look at the graph of \(e^x\)

Answer 5

would it be -infinity?

Answer 6

no...for any real x we have \(e^x>0\)

so it can't be \(-\infty\)

Answer 7

looks something like this

Answer 8

\[
\lim_{x\to-\infty}e^x = 0 \\
\lim_{x\to-\infty}\frac{6}{e^x+7} = \frac{6}{0+7} = \frac 67
\]