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Arthur
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4
Solve the following differential equation : $\frac{d^3y}{dx^3}+y=3+e^{-x}+5e^{2x}.$
Apr 5, 2023
4
Let $F_m$ be the $mth$ Fibonacci number given by $F_1=F_2=1$ and $F_{m+2}=F_m+F_{m+1}$ for all $m\geq 1.$ Show that $\sum\binom nk=F_{m+1},$ [duplicate]
Apr 7, 2023
4
Find the number of distinct integers in the collection of first $500$ terms of each of the arithemetic progressions $\{1,4,...\}$ and $\{9,14,...\}$
Apr 1, 2023
4
Find a formula for the $nth$ non-square positive integer, in terms of $n.$
Apr 13, 2023
4
Given the curve $y=\frac{5x}{x-3}$. Find its asymptotes, if any.
Jan 8, 2023
4
Let $[x]$ denote the greatest integer function. Find the value of $\int_0^{n^{\frac1k}}[x^k+n]dx.$
Apr 27, 2023
4
Evaluate $\displaystyle\lim_{n\to \infty}\left [\left (1+\frac{2}{n^a}\right )^{-n^b}n^c\right ]$ for real $a,b,c$ and $n\geq 1$.
Apr 29, 2023
3
Meaning of the notation $[G : H]$ in group theory .
Dec 26, 2022
3
Let $f(x)=x^n+p_1x^{n-1}+p_2x^{n-2}+ ...+p_n.$ The positive roots of the equation $f(x)=0$ do not exceed $\sqrt[r]{p}+1$ where $-p$ is the greatest
Dec 17, 2022
3
Solve the following differential equation: $\frac{d^2y}{dx^2}+a^2y=\cos ax.$
Apr 8, 2023