Help Finding Lim x=> infinity 3e^3x+2e^x-1 / e^3x-e^2x+5

[roksteady]

I need help finding the answer to this

-Use the limit laws to find the limit if it exists:


Lim x=> infinity 3e^3x+2e^x-1 / e^3x-e^2x+5


Any help would be a big help, thanks

 

[Unco]

Re: Help Finding Limits!!!

G'day, Roksteady. For future posts, be sure to use parentheses. In this case the expression in the limit is typed: (3e^(3x) + 2e^x - 1)/(e^(3x) - e^(2x) + 5).

To find the limit, simply divide both the numerator and the denominator by e^(3x), and apply the "limit laws".

 

[PAULK]

I need help finding the answer to this

-Use the limit laws to find the limit if it exists:


Lim x=> infinity 3e^3x+2e^x-1 / e^3x-e^2x+5


Any help would be a big help, thanks

For Lim x=> infinity of:
3e^3x+2e^x-1
-----------------
e^3x-e^2x+5

let y = e^x

3y^3 + 2y - 1
--------------
y^3 - y^2 + 5

Now use the standard 'complex fraction trick': Divide every term by y^3

3 + 2/y^2 - 1/y^3
--------------------
2 - 1/y + 5/y^3

Now observe that if x => inf, y => inf as well. You can finish up.