14
Nov
2020
Question of the Day
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With the help of Rolle’s Theorem and the function $f\left(x\right)=e^{-x} \left(x-a\right)\left(x-b\right)$ prove that the equation $\left(x-a\right)\left(x-b)=\left(x-a\left)+\left(x-b\right)$ will have a solution in the set $\left(a,b\right)$ where $a < b$.
13
Nov
2020
Question of the Day
Does the following converge or diverge? $\int_{0}^{\infty} e^{-x} dx$
12
Nov
2020
Question of the Day
Prove that polynomials with real coefficients and odd degree always have at least one real root.
11
Nov
2020
Question of the Day
Find the Maclaurin Series of $\frac{4x^2-3}{\left(1-x\right)\left(1-2x\right)^2}$ where $x$ is small i.e. less than $\frac{1}{2}$ in magnitude. But, you can’t use the formula for the Maclaurin Series however you may use the fact that $\frac{1}{1-x} = 1 + x + x^2 + x^3 + \cdots $.
10
Nov
2020
Question of the Day
Find a cubic approximation for the $\tan x$ when $x$ is small, i.e. $|x|<\frac{\pi}{2}$.
9
Nov
2020
Question of the Day
Find the Taylor Series of $\frac{1}{\left(1-x\right)^2}$
8
Nov
2020
Question of the Day
Derive the Taylor Series Expansion (there is no need to find the remainder term / discuss convergence etc.)
7
Nov
2020
Question of the Day
Will the following converge or diverge? $\sum\limits_{n=1}^\infty \frac{ x^n }{ n^2 } $
6
Nov
2020
Question of the Day
Will the following converge or diverge? $\sum\limits_{n=1}^\infty \frac{ n }{ 3n^2 – 1 } $
5
Nov
2020
Question of the Day
Will the following converge or diverge? $\sum\limits_{n=1}^\infty \frac{ n^2 + 1 }{ n^5 + n + 1 } $