Category: Relation and Functions

Question Number 329 by 123456 last updated on 23/Dec/14 $$\underset{0}{\stackrel{x}{\int }}f\left(t\right)dt+\underset{x}{\stackrel{2x}{\int }}tf\left(t\right)dt=\underset{0}{\stackrel{2x}{\int }}(1-t)f\left(t\right)dt$$$$f\left(\frac{1}{2}\right)=?$$ Commented by prakash jain last…

Question Number 303 by 123456 last updated on 25/Jan/15 $$f(x,y,z)=\frac{y^2{z}^3}{1-x}+\frac{{xz}^3}{1-y^2}+\frac{{xy}^2}{1-z^3}$$$$\mathrm{find}$$$$\frac{\partial f}{\partial x}+\frac{\partial f}{\partial y}+\frac{\partial f}{\partial z}$$ Answered by prakash…

Question Number 291 by 123456 last updated on 25/Jan/15 $$a(n,m)=\{\begin{array}{ll}m& n⩽0\\ a(n-1,m+2)& n>0\wedge n\equiv 0\left(\mathrm{mod}2\right)\\ a(n-2,m-1)+nn& n>0\wedge n\equiv 1\left(\mathrm{mod}2\right)\wedge m⩽0\\ a(m-1,n-1)+a(n-2,m-2)& n>0\wedge n\equiv 1\left(\mathrm{mod}2\right)\wedge m>0\end{array}$$$$\mathrm{evaluate}a(7,5)$$ Answered by prakash jain last updated on 19/Dec/14 $$a(7,5)=a(4,6)+a(5,3)$$$$={a}\left(\mathrm{3},\mathrm{8}\right)+{a}\left(\mathrm{2},\mathrm{4}\right)+{a}\left(\mathrm{3},\mathrm{1}\right)…

Question Number 257 by abcd last updated on 25/Jan/15 $$\mathrm{If}\mathrm{f}\left(x\right)\mathrm{is}\mathrm{a}\mathrm{function}\mathrm{satisfying}$$$$\mathrm{f}(\mathrm{x}+\mathrm{y})=\mathrm{f}\left(\mathrm{x}\right)\mathrm{f}\left(\mathrm{y}\right)\mathrm{for}\mathrm{all}\mathrm{x},\mathrm{y}\in \mathbb{N}\mathrm{such}$$$$\mathrm{that}\mathrm{f}\left(1\right)=3\mathrm{and}\underset{x=1}{\sum ^n}\mathrm{f}\left(\mathrm{x}\right)=120.\mathrm{Then}\mathrm{find}$$$$\mathrm{the}\mathrm{value}\mathrm{of}n.$$ Answered by 123456 last updated…

Question Number 65779 by mathmax by abdo last updated on 03/Aug/19 $$calculate{lim}_{x\to 0}\frac{sin\left(x^2\right)-xtan\left(x\right)}{1-cos\left(4x\right)}$$ Commented by mathmax by abdo last updated on 04/Aug/19…