Tuesday, March 7, 2017

Single Variable Calculus, Chapter 7, 7.8, Section 7.8, Problem 20

Determine the limx1lnxsinπx. Use L'Hospital's Rule where appropriate. Use some Elementary method if posible. If L'Hospitals Rule doesn't apply. Explain why.

limx1lnxsinπx=ln(1)sin[(π)(1)]=0sinπ=00 Indeterminate form

Thus, by applying L'Hospital's Rule...

limx1lnxsinπx=limx1xddx(lnx)ddxsinπ(x)=limx11xcosπxπ=limx11πxcos(πx)=1π(1)cos(π(1))=1πcos(π)=1π(1)=1π

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