- #1

LemuelUhuru

- 6

- 0

## Homework Statement

Suppose ##f(x)## and ##g(x)## [itex]\rightarrow[/itex] 0 as x [itex]\rightarrow[/itex] 0+. Find examples of functions f and g with these properties and such that:

a.) ## \lim_{x\rightarrow 0+} { f(x)^{g(x)} = 0 } ##

## Homework Equations

None

## The Attempt at a Solution

Let ## f(x) = 2^x-1 ## and ## g(x) = x ##

## \displaystyle \lim_{x\rightarrow 0+} ({2^x-1})^{x} = (2^{x^2}-1^{x}) = (1-1) = 0##

My experience with limits is basic, recently while experimenting with expressions approaching infinity I was told that if you obtain an indeterminate then you need to further simplify the expression, in this case substituting x for zero immediately reduced my expression to one which is an determinate. I imagine this means there is no need to simplify and that my solution is invalid, therefore I am confused on how to proceed.

Thank you in advanced for the help.