Mathematics Questions, Problems & Solutions : TransWikia.com ~ Page 82

Can $y=10^{-x}$ be converted into an equivalent $y=mathrm{e}^{-kx}$?

I was dealing with the values:| Digits | Expression | Value ||--------|------------|-----------------------|| 1...

Asked on 11/16/2021

4 answer

Solving $left(x-c_1frac{d}{dx}right)^nf(x)=0$ for $f(x)$

I'm given that $$left(x-c_1frac{d}{dx}right)^nf(x) = 0$$ I have to solve for $f(x)$ in terms of $n$.For $n=0$:$$f(x)=0 tag{0}$$For $n= 1$:$$begin{align}xf(x)...

Asked on 11/16/2021

3 answer

What is an intuitive approach to solving $lim_{nrightarrowinfty}biggl(frac{1}{n^2} + frac{2}{n^2} + frac{3}{n^2}+dots+frac{n}{n^2}biggr)$?

$$lim_{nrightarrowinfty}biggl(frac{1}{n^2} + frac{2}{n^2} + frac{3}{n^2}+dots+frac{n}{n^2}biggr)$$I managed to get the answer as $1$ by standard methods of solving, learned from teachers, but my intuition says that the denominator of every term...

Asked on 11/16/2021

11 answer

Why does the Binomial Theorem use combinations and not permutations for its coefficients?

I have been trying to understand the Binomial Theorem formula. I can see that it works. What I don’t understand is how or why using combinations...

Asked on 11/16/2021 by Jor

5 answer

The convergence of the improper integral $int_{0}^inftyfrac{sin^2(x)}{x^{5/2}},dx$

I have to analyse the convergence of $int_{0}^inftyfrac{sin^2(x)}{x^{5/2}},dx$.What I have done is: First of all, I've divided the integral in two integrals: $int_{0}^inftyfrac{sin^2(x)}{x^{5/2}},dx=int_{0}^{1}frac{sin^2(x)}{x^{5/2}},dx+int_{1}^inftyfrac{sin^2(x)}{x^{5/2}},dx$ I've analysed the second integral:...

Asked on 11/16/2021

3 answer

Taking the matrix derivative of the product of one matrix and a Hadamard Product.

Consider the three matrices $mathbf{C}$, $mathbf{A}$, and $mathbf{T}$. The matrix $mathbf{C}$ has $mathit{m} times mathit{k}$ entries, $mathbf{A}$ is a $mathit{k} times mathit{n}$ matrix,...

Asked on 11/16/2021

2 answer

Is Basic Mathematics by Serge Lang rigorous?

Does Basic Mathematics give a suitably rigorous treatment of algebra and geometry topics covered in high school? Does it prepare the reader for more difficult texts like...

Asked on 11/16/2021 by bonsoir

1 answer

Variance Estimator in Simple Random Sampling Without Replacement

I have to find the unbiased estimator of population variance under simple random sampling without replacement. The hint for the demonstration is:$$ frac{1}{N} sum_{k =1}^{N} (x_{k} -...

Asked on 11/16/2021 by Guilty_Scene

1 answer

Has anyone attempted solving the Poincaré conjecture using Lie groups?

Among the many unsuccessful attempts at solving the Poincaré conjecture, I'm wondering if there was an approach that went along the lines of showing that a closed simply connected ...

Asked on 11/16/2021 by Paul Cusson

0 answer

General integral $int_0^{frac{pi}{p}}lntan x ,dx $

I was motivated by the integral $displaystyle int_0^{pi/12} lntan(x),dx$ which was posted here which is equal to $-frac{2}{3}G$ where is $G$ is Catalan's constant.With...

Asked on 11/16/2021 by Naren

3 answer

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