One of my colleagues placed the following problem on an exam for his Calculus II course…

and was impressed by the variety of correct responses that he received. I thought it would be fun to discuss some of the different ways that this limit can be computed.

Method #3. A trigonometric identity. When we see inside of an integral, one kneejerk reaction is to try the trigonometric substitution . So let’s use this here. Also, since , we can change the limit to be :

I'm a Professor of Mathematics and a University Distinguished Teaching Professor at the University of North Texas. For eight years, I was co-director of Teach North Texas, UNT's program for preparing secondary teachers of mathematics and science.
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