i have been curious about prime numbers lately and have been wondering what is the smallest prime number that is made of consecutive numbers as its digits...
I'm trying to find the exact value of $$\int_{\frac{1}{\sqrt{3}}}^{\sqrt{3}} \frac{\arctan{(x^2)} }{1+x^2} \, dx$$ Ostensibly, I'd want to use t...
I'd like to solve $AX -BX + XC = D$, for the matrix $X$, where all matrices have real entries and $X$ is a rectangular matrix, while $B$ and $C$ are ...
I have been searching for information about that conjecture and it seems for me that noone has made any significant improvement on it in the last 30 years...
I'd like to see an example of a second-order markov chain. Haven't found one over google or in any of my textbooks.
Question: What is appropriate notation for calculating the mode of a function? In this case, I use the mode of a Gamma(a,b) distribution in a cost-functio...
I need to find a formula for the nth term in the sequence $\frac{2}{3}, \frac{3}{5}, \frac{4}{7}, \frac{5}{9}, \frac{6}{11}$ I have tried the usual approa...
What is the limit of $\sin^{-1} (\sec x) $ as $x$ tends to $0$. By direct substitution the value of $\sec x $ at $x =0$ is $1$. So limit should be $1$. Bu...
I'm taking single variable calculus on Coursera platform and asked : Write first four terms of the sum : $$ \sum_{k=1}^\infty \frac{(-1)^{k+1(2^k)}}{...
80 students were asked if they like math, science or humanities. 24 students did not like either of the subjects, 9 liked math only, 16 liked science only...
I open an account at a bank with 1% interest compounded monthly. I'm adding $100 to it at the beginning of each month (starting with month 1). (a) Se...
The term of relative degree is used a lot in books of control systems. I need some explaining to understand the useful and effect of the relative degree o...