# Math Help - LImits at infinity help: Indeterminate forms

1. ## LImits at infinity help: Indeterminate forms

Help with these: Find the limit if it exists

2. do you know L'Hopital's rule?

3. Number 3 has an answer similar to this:

Question: how did (2x-1)/(2sqrt(x^2-x)) became 1?

4. Originally Posted by ^_^Engineer_Adam^_^
Number 3 has an answer similar to this:

Question: how did (2x-1)/(2sqrt(x^2-x)) became 1?
for x>0

sqrt(x^2-x)=x*sqrt(1-1/x)

now simplify (2x-1)/(2sqrt(x^2-x)) and take the limit.

5. Is The answer of number 1 e^1? and thanks
no need for 2 & 3 ive already answered it

6. Originally Posted by ^_^Engineer_Adam^_^
Is The answer of number 1 e^1? and thanks
no need for 2 & 3 ive already answered it

No (1) diverges.

Take logs and then consider the limit of x^2 ln(1+1/(2x)) using L'Hopital's rule.

RonL

7. The answer of no. 1 is e^(-4)? Isnt it?

8. Originally Posted by ^_^Engineer_Adam^_^
The answer of no. 1 is e^(-4)? Isnt it?
(1+1/(2*10))^(10^2) ~= 131

(1+1/(2*100))^(100^2) ~= 4.6 10^21

L'Hopital says it diverges, and numerical experiment supports that.

RonL