Question

Can someone please explain this limit to me?

Answer 1

and why when x>1 the limit is infinity

Answer 2

as x->1 the limit is infinity, because 1/0 goes to infinity and e^infinity goes to infinity

Answer 3

i wanted to know the difference between the 2 cases, when x is greater than 1 and when x is less than 1...

Answer 4

did u mean when x approaches from \(1^{+}\) and \(1^{-}\)

Answer 5

this is what i mean

Answer 6

i guess this


means the \(x \rightarrow 1\) from left as well as right

Answer 7

when it comes from \(x<1\) it comes from the left negative \(1^{-}\)and

when it comes from \(x>1\) it comes from the positive \(1^{+}\)

Answer 8

so when
\(\large \begin{align} \color{black}{\lim_{x\to1^{-}}e ^{\frac{1}{x^2-1}}\hspace{.33em}\\~\\
=e^{-\infty }\hspace{.33em}\\~\\
=0
}\end{align}\)

Answer 9

and
\(\large \begin{align} \color{black}{\lim_{x\to1^{+}}e^{\frac{1}{x^2-1}}\hspace{.33em}\\~\\
=e^{+\infty }\hspace{.33em}\\~\\
=\infty
}\end{align}\)