24
Nov
2020
Question of the Day
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Show that $\sum\limits_{n=1}^\infty \frac{\sin n}{ n } $ converges.
23
Nov
2020
Question of the Day
Prove that the remainder $R_k$ in the Taylor series expansion of $\cos x$ at the point $a=0$ will converge for all values of $x$ in $\mathbb{R}$.
22
Nov
2020
Question of the Day
Find the limit of $ \lim\limits_{n \to \infty } \frac{r^n}{n!} $, where $r$ is a positive real non-zero number.
21
Nov
2020
Question of the Day
Prove that $-\pi+\sqrt{5+\pi^2}$ is irrational.
20
Nov
2020
Question of the Day
Find the limit of $ \lim\limits_{n \to \infty } \sqrt[n]{n} $.
19
Nov
2020
Question of the Day
Calculate the upper and lower Riemann Sum for the function $f\left(x\right)=1$ when $x$ is rational and $f\left(x\right)=-1$ when $x$ is irrational. Hence show that this function is not Riemann-integrable.
18
Nov
2020
Question of the Day
Calculate the limit \lim\limits_{x \to 0 } x \ln x without using L’Hôpital’s rule.
17
Nov
2020
Question of the Day
Does the following converge or diverge? $\int_{0}^{1} \ln x dx$
16
Nov
2020
Question of the Day
Does the following converge or diverge? $\int_{0}^{1} x^{-1} dx$
15
Nov
2020
Question of the Day
Does the following converge or diverge? $\int_{0}^{1} x^{-\frac{1}{2}} dx$