1.
In order to satisfy the conditions of the comparison test, if you want to show your original series diverges, you need something smaller or equal to. You can *guarantee* that the series you are comparing it to will be smaller by taking something with a larger coefficient than the 4j, such...
Consider: What are both of the functions doing as X-> pi/2?
As you are in precalc and not expected to use L'Hopitals Rule, look at the graphs of these functions and consider which has larger values as X-> pi/2
If you have a very small value in the numerator and a larger value in the...
Hint:
Many functions modeling bacterial growth, population growth, decay, use natural logs and the inverse function of natural logs, (about as close as a hint as I can give without naming it), and exponentials. Thinking around these lines, what function involving the aforementioned general...
Hint:
Many functions modeling bacterial growth, population growth, decay, use natural logs and the inverse function of natural logs (about as close as a hint as I can give without naming it). Thinking around these lines, what function involving the aforementioned general family has a derivative...
Homework Statement
This is not so much an entire problem I need help with but just a part.
It is a power series where after you do the ratio test, you end up with |4x^(2)| < 1, so |x^(2)| < 1/4.
Since the radius of convergence is |x-a| < R, I end up with -1/4 < x^(2) < 1/4, but because...