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.1/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 ?⁰ so let f(x) = ^1/x and take logarithms of both sides
ln f(x) = (1/x) ln  = 
ln f(x)   =   
 =  differentiate
 =    = 0

So  ^1/x  = e^{ln f(x)}  = e⁰  = 1