Question

Evaluate the following limits.

(a)
limx→∞(4/(ex−9))=

Answer 1

please help me!!?

Answer 2

put x=1/y
\[y \rightarrow0\]
\[\lim_{x \rightarrow \infty}\frac{ 4 }{ex-9 }=\lim_{y \rightarrow 0}\frac{ 4 }{ \frac{ e }{y }-9 }\]
\[=\lim_{y \rightarrow0}\frac{ 4y }{e-9y }=\frac{ 4*0 }{e-9*0 }=\frac{ 0 }{e }=0\]

Answer 3

what will happen if it goes to the -infinity, if you don't mind me asking @surjithayer

Answer 4

still the answer remains the same

Answer 5

If you want to be technical about it, as it goes to infinity we have positive finite / positive infinite => +0.

As it goes to negative infinity, we have a positive finite / negative infinity => -0.

The answer is still the same, however it is something you might want to consider when evaluating certain limits. For example, if I were to ask the limits of 1/ (4/(e*x−9) or 1/ *your original limit* - without bringing (e*x-9) up (so that 1/4/(e*x-9) becomes (e*x-9)/4)
by knowing the previous limit you could pretty much reduce it to 1/0. However, whether that 0 is a +0 or a -0 is relevant here, because the answer to 1/0 will be either +infinite or -infinite accordingly.