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 :