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.
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