- #1
Chandasouk
- 165
- 0
I know L'Hoptal's rule can only be use when you have indeterminate forms and such, but I do not know how to make a limit a fraction sometimes. Take this limit for example:
The limit at which X approaches infinity of (1+[tex]\frac{1}{x}[/tex])X
I make y = The limit at which X approaches infinity of (1+[tex]\frac{1}{x}[/tex])X
Take the Ln of both sides to get
lny = X*ln(1+[tex]\frac{1}{x}[/tex])
which can be rewritten as ln(1+1/x)/(1/x) but how? I get lost in the algebra and don't know how to obtain that.
The limit at which X approaches infinity of (1+[tex]\frac{1}{x}[/tex])X
I make y = The limit at which X approaches infinity of (1+[tex]\frac{1}{x}[/tex])X
Take the Ln of both sides to get
lny = X*ln(1+[tex]\frac{1}{x}[/tex])
which can be rewritten as ln(1+1/x)/(1/x) but how? I get lost in the algebra and don't know how to obtain that.