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Hey guys, I have a few problems I need help with and answers checked.
Problem 1. Calculate each limit.
a.
My Solution
Form , Using L'Hopital's Rule.
b.
My Solution
Form , Using L'Hopital's Rule. = , Using L'Hopital's Rule.
c.
My Solution
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?
d.
My Solution
Let
= 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.
a.
My Solution
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?
b.
My Solution
Here I run into the same problem as in 2a.
Any and all help would be much appreciated. Thanks in advance.
As far as I can tell, b is correct. For c I'll start with your consolidated form of it:
Using L'Hopital's rule, we must differentiate the function:
This is because we must differentiate the numerator and denominator separately, so that:
So, we use L'Hopital's rule again, getting:
So that:
So, Random Variable is right on b.