Here comes the last part of the Limits and Integrals series, previous ones can be found here: Part 1 and Part 2. This time we will discuss even more challenging limits, so get ready and have fun!
The next problem was found in "A Note on Evaluating Limits Using Riemann Sums" by Sudhir K. Goel and Dennis M. Rodriguez.
Problem 7. Evaluate
Solution. After mastering several similar problems there should be no dificulty in applying our technique to this one.
Even slightest knowledge of integrals suggest that something went wrong. Actually everything is just fine, but the intgeral we need to evaluate is an improper one. Now let's proceed to finish it
Now let's move onto the next example.
Problem 8. Calculate
Solution. This one will be a tough task, but after eight solved examples nothing is imposible.
Now we need to get rid of the function. Many of you proably know that near the function behaves just like . This fact is proven by computing Taylor Series of at the point .
The last problem in this series of posts we'll be following one.
Problem 9. Find the limit