Question of the Day
Posted on07 Jan 2021
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Prove that $e^a (b-a) < e^b – e^a < e^b(b-a)$ for all $a<b$ in $\mathbb{R}$.
Question of the Day
Posted on06 Jan 2021
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Consider the non-zero real-valued function $exp$ on the reals such that $exp(a+b)=exp(a)exp(b)$ and $exp'(a)=exp(a)$ for all real values of $a$ and $b$.... Read More
Question of the Day
Posted on05 Jan 2021
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Where does the following converge $\int_{1}^{\infty} e^{-\alpha x} dx$?
Question of the Day
Posted on04 Jan 2021
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For what values of $\alpha$ will $\int_1^\infty \! x^{-\alpha} \, \mathrm{d}x$ converge?
Question of the Day
Posted on03 Jan 2021
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Show that $f(x) = x^4 – 3x^2 + 1$ has two positive and two negative roots.
Question of the Day
Posted on02 Jan 2021
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Test for absolute convergence: $\displaystyle\sum_{n=1}^{\infty}\frac{n! (x-2)^n}{ n^2 }$
Question of the Day
Posted on01 Jan 2021
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Test for absolute convergence: $\displaystyle\sum_{n=1}^{\infty}\frac{(x-4)^n}{ n }$
Question of the Day
Posted on31 Dec 2020
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Test for absolute convergence: $\displaystyle\sum_{n=1}^{\infty}\frac{2^n x^n}{ n^2 }$
Question of the Day
Posted on30 Dec 2020
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Consider the sequence $ x_{n} = \frac{1}{n} $ if $n$ is odd and $x_{n} = 1$ if $n$ is even. Does this... Read More
Question of the Day
Posted on29 Dec 2020
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Consider the sequence $ x_{n} = \frac{1}{n} $ if $n$ is odd and $x_{n} = 0$ if $n$ is even. Does this... Read More