Thread: LImits at infinity help: Indeterminate forms

Help with these: Find the limit if it exists

do you know L'Hopital's rule?

Number 3 has an answer similar to this:




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

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.

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

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

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

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