Recent content by cbarker1

You may have an equivalent answer to the book. There are so many equivalent answers to one indefinite integrals. I recommend you to take the derivative of your answer to see if it is your integrand.

I am reading Sheldon's Axler Book on Measure theory. He is proving that ##L^p(\mu)## is a Vector space over ##\mathbb{R}.## He claims that if ##\|f+g\|_{p}^p\leq 2^p(\|f\|_{p}^p+\|g\|_{p}^{p})## and nonzero homogenity holds true, then ##L^p{\mu}## is true with the standard addition and scalar...

ok. thanks for your input. But, I think you may not answer my question because I am wondering how to do the partial fraction decomposition with respect to residue theory in complex analysis the multiple roots case?

Dear Everybody, I am wondering how to compute the partial fraction decomposition of the following rational function: ##f(z)=\frac{z+2}{(z+1)^2(z^2+1)}.## I understand how to do the simple poles of the function and how it is related to the decomposition's constants, i.e...

Dear Everybody, I am having trouble with last part of this question. I believe the answer is no. But I have to proof the general case. Here is my work for the problem: Suppose that we have two distinct norms on the same vector space ##X## over complex numbers. Then there exists no ##K## in...

Dear everybody, I am having some trouble proving the implication (or the forward direction.) Here is my work: Suppose that we have an arbitrary linear functional ##l## on a Banach Space ##B## is continuous. Since ##l## is continuous linear functional on B, in other words, we want show that...

Dear everyone, I am having trouble with this problem. I have convinced myself that the ##a^t-a\leq 0## is true. Now, I am trying to applying this inequality for the finite series and I don't know where to start. After that, proving that the p-norm is less or equal to the q-norm. Thanks...

I forgot to add that my professor wrote the problem.

Dear Everybody, I am working on my homework. I am trying to prove a problem that was written by my professor in an odd way: Prove that when p is true, then q is true. Which proposition statement should I assume? I personally thought that I should assume the first one. But reading my...

yes. I do.

See the work below: I feel like it that I did it correctly. I feel like I skip a step in my induction. Please point any errors.

Mostly Teaching licenses in my state. They might have to pass college algebra to go to the next course (business math course), or the nursing students might have to pass college algebra to go into elementary stats.

No malicious issues from this pdf, it is just a list of course.

Here is the list of course that satisfy this requirement.

In my school, in our liberal arts requirement for critical thinking, you can do philosophy or mathematics-college algebra, pre-cal, calculus 1, trigonometry, or math perspective courses. Some people have to take it for there education degree as requirement to get license in my state.