Estimate the limit by graphing the function for an appropriate domain. Confirm your estimate by using l'Hopital's rule. Show each step of your calculation.x

Question

What will be an ideal response?

Answer 1

Using the graph, students should estimate the limit to be 1.

Using l'Hopital's rule: 
the limit leads to the indeterminate form 0⁰ so let f(x) = x and take logarithms of both sides
ln f(x) =  ln x  = 
ln f(x)   =   
 =  differentiate
 =  -2  = 0

So  x  = e^{ln f(x)}  = e⁰  = 1