Recent content by cbarker1

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    I What is the name of this geometry theorem?

    I think it is called the law of Sines, since you are given SSA conditions on the triangle. This case is called the ambiguous case because there could be 0,1, 2 triangles. cbarker1
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    LaTeX Creating a right triangle in Cartesian plane in LaTeX

    Dear everybody, I am trying to create a right triangle in Cartesian plane with no grid lines in Latex. I have no way to start it. I am having a hard time. I want to use tikz picture. Thanks, cbarker1
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    A Proving that this integral is divergent

    Dear everyone, I have a question on how to show that an integral is divigent. Here is the setup: Suppose that we have the following function ##\sigma(x)=\frac{1}{x^{2-\varepsilon}}## for an arbitrary fixed ##\varepsilon>0.## \begin{equation}...
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    I'm getting the wrong answer for the Indefinite Integral of: (x^2+2x)/(x+1)^2

    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.
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    A Why the triangle inequality is greater than the 2 max{f(x),g(x)}

    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...
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    I Using Residues (Complex Analysis) to compute partial fractions

    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?
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    I Using Residues (Complex Analysis) to compute partial fractions

    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...
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    Does each norm on vector space become discontinuous when restricted to S^1?

    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...
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    Help Needed Proving Implication for Linear Functional on Banach Space

    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...
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    Prove that l^p is a subset of l^q for all p,q from 1 to infinity

    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...
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    I Equivalence Question between when-then statement and if then statement

    I forgot to add that my professor wrote the problem.
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    I Equivalence Question between when-then statement and if then statement

    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...
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    Prove by induction the sum of complex numbers is complex number

    yes. I do.
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    Prove by induction the sum of complex numbers is complex number

    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.
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    How to lower one's expectation in teaching college algebra

    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.