Category: Relation and Functions

Question Number 28977 by abdo imad last updated on 02/Feb/18 $$letgive{u}_n=\sum _{k=1}^n{a}_k^{2}with\left(a_k\right)sequenceofreals/a_{k>0}$$$${and}\:{v}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{a}_{{k}} }{{k}}\:.\:{prove}\:{that}\:{u}_{{n}} {converges}\Rightarrow\left({v}_{{n}} \right){converges}…

Question Number 28858 by amit96 last updated on 31/Jan/18 Commented by abdo imad last updated on 31/Jan/18 $$wehavef\left(x\right)=x^3+xandg\left(x\right)=x^3-x\Rightarrow$$$${f}^{'} \left({x}\right)=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}\:{and}\:{g}^{'} \left({x}\right)=\mathrm{3}{x}^{\mathrm{2}}…

Question Number 94374 by Jidda28 last updated on 18/May/20 $$\mathrm{In}7\mathrm{yrs},\mathrm{Haidar}\mathrm{senior}\mathrm{Kani}\mathrm{with}3\mathrm{yrs}.$$$$\mathrm{In}\mathrm{the}\mathrm{next}4\mathrm{yrs}\mathrm{Haidar}\mathrm{again}\mathrm{seniors}\mathrm{Kani}$$$$\mathrm{with}2\mathrm{yrs}.\mathrm{How}\mathrm{old}\mathrm{is}\mathrm{Haidar}\mathrm{and}\mathrm{Kani}?$$ Commented by Rasheed.Sindhi last updated on 18/May/20 $${If}\:\:{in}\:\mathrm{7}{yrs}\:{Haidar}\:{senior}\:{Kani} \…

Question Number 94340 by mathmax by abdo last updated on 20/May/20 $$1)\mathrm{calculate}{\mathrm{U}}_{\mathrm{n}}={\int }_0^1\ln \left(\mathrm{x}\right)\ln (1-\frac{\mathrm{x}}{\mathrm{n}})\mathrm{dx}(\mathrm{n}>0)$$$$2)\mathrm{find}\mathrm{nature}\mathrm{of}\mathrm{\Sigma }{\mathrm{U}}_{\mathrm{n}}\mathrm{and}\mathrm{\Sigma }{\mathrm{nU}}_{\mathrm{n}}$$ Answered by abdomathmax last updated…

Question Number 94336 by mathmax by abdo last updated on 19/May/20 $$\mathrm{let}\mathrm{f}\left(\mathrm{x}\right)=\arctan \left(2\mathrm{x}\right){\mathrm{e}}^{-3\mathrm{x}}$$$$1)\mathrm{determine}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(\mathrm{x}\right)\mathrm{and}{\mathrm{f}}^{\left(\mathrm{n}\right)}\left(0\right)$$$$2)\mathrm{developp}\mathrm{f}\mathrm{at}\mathrm{integr}\mathrm{serie}$$ Answered by prakash jain last…