Question: We'll evaluate the limitlimx(1+1x)x.(a) Explain why this doesn't look like an indeterminate form we've been using.(b) Let's call this limity.Ifwe take the lnof both sides,

We'll evaluate the limitlimx(1+1x)x.(a) Explain why this doesn't look like an indeterminate form we've been using.(b) Let's call this limity.Ifwe take the lnof both sides, we can write:ln(y)=ln(limx(1+1x)x).In fact, thanks to continuity, we can writeln(y)=limxln((1+1x)x).Show the steps we need to rewrite the right-hand side aslimxln(1+1x)1x(c) Show that this does give usan indeterminate form, and then evaluate the limit usingL'hpital's rule.(d) Finally, solve for y. Sometimes this limitis used as the definition of this famous number.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Mathematics Questions!