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 :

.

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*Posted by John Quintanilla on September 25, 2015*

https://meangreenmath.com/2015/09/25/different-ways-of-computing-a-limit-part-3/