Limits of Indeterminate Forms and Improper Integrals
Hey guys, I have a few problems I need help with and answers checked.
Problem 1. Calculate each limit.
Form , Using L'Hopital's Rule.
Form , Using L'Hopital's Rule. = , Using L'Hopital's Rule.
I'm having trouble with this one.
Form , Using L'Hopital's Rule. ... This is also of the form . I've applied L'Hopital's Rule two more times and it just keeps getting nastier and nastier but is still keeping the form . Where am I going wrong?
= Form , Using L'Hopital's Rule. = (Shortening the simplifying steps due to me not wanting carpal tunnel syndrome.) =
Problem 2. Determine whether the improper integral converges, or diverges. In the case of convergence, give its value.
u = lnx, du = dx, dv = dx, v = x
Here I don't know what I'm supposed to do. How am I supposed to get the limit if I have both x's and t's?
Here I run into the same problem as in 2a.
Any and all help would be much appreciated. Thanks in advance.