Menu Close

Category: None

Question-156933

Question Number 156933 by CAIMAN last updated on 17/Oct/21 Answered by mindispower last updated on 17/Oct/21 $$\frac{\mathrm{1}}{{t}}={x} \\ $$$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\frac{\mathrm{1}}{\mathrm{3}}} \frac{{ln}\left({x}\right)}{{x}\left(\mathrm{1}+{x}\right)}{dx}=\int\frac{{ln}\left({x}\right)}{{x}}−\frac{{ln}\left({x}\right)}{\mathrm{1}+{x}}{dx} \\ $$$$=\frac{{ln}^{\mathrm{2}} \left({x}\right)}{\mathrm{2}}−{ln}\left({x}\right){ln}\left(\mathrm{1}+{x}\right)+\int\frac{{ln}\left(\mathrm{1}+{x}\right)}{{x}}{dx} \\…

k-2-k-3-1-k-3-1-

Question Number 156924 by cortano last updated on 17/Oct/21 $$\:\underset{{k}=\mathrm{2}} {\overset{\infty} {\prod}}\:\left(\frac{{k}^{\mathrm{3}} −\mathrm{1}}{{k}^{\mathrm{3}} +\mathrm{1}}\right)\:=? \\ $$ Answered by puissant last updated on 17/Oct/21 $${P}=\underset{{k}=\mathrm{2}} {\overset{\infty}…

How-many-eleven-digits-palindrome-numbers-can-be-formed-by-0-2-3-4-and-8-Zero-in-the-middle-of-order-always-

Question Number 91336 by naka3546 last updated on 30/Apr/20 $${How}\:\:{many}\:\:{eleven}\:\:{digits}\:\:{palindrome}\:\:{numbers}\:\:{can}\:\:{be} \\ $$$${formed}\:\:{by}\:\:\mathrm{0},\:\mathrm{2},\:\mathrm{3},\:\mathrm{4},\:\:{and}\:\:\mathrm{8}\:? \\ $$$${Zero}\:\:{in}\:\:{the}\:{middle}\:\:{of}\:\:{order}\:\:{always}\:. \\ $$ Commented by jagoll last updated on 30/Apr/20 $$\mathrm{4}!\:=\:\mathrm{24}\: \\…

Find-the-sum-9-1-2-10-2-2-3-10-3-3-4-10-99-99-100-x-the-greatest-integer-function-

Question Number 91328 by Maclaurin Stickker last updated on 30/Apr/20 $${Find}\:{the}\:{sum} \\ $$$$\frac{\mathrm{9}}{\mathrm{1}+\sqrt{\mathrm{2}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{2}}\rfloor}{\:\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}}+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{3}}\rfloor}{\:\sqrt{\mathrm{3}}+\sqrt{\mathrm{4}}}+…+\frac{\mathrm{10}−\lfloor\sqrt{\mathrm{99}}\rfloor}{\:\sqrt{\mathrm{99}}+\sqrt{\mathrm{100}}} \\ $$$$\lfloor{x}\rfloor={the}\:{greatest}\:{integer}\:{function} \\ $$ Commented by Prithwish Sen 1 last updated on…

1-find-eigen-values-and-corresponding-eigen-vector-of-the-matrix-A-cos-sin-sin-cos-2-solve-6y-2-dx-x-y-2x-2-dy-0-

Question Number 91321 by  M±th+et+s last updated on 29/Apr/20 $$\left.\mathrm{1}\right){find}\:{eigen}\:{values}\:{and}\:{corresponding} \\ $$$${eigen}\:{vector}\:{of}\:{the}\:{matrix} \\ $$$$ \\ $$$${A}=\begin{bmatrix}{{cos}\left(\theta\right)}&{−{sin}\left(\theta\right)}\\{{sin}\left(\theta\right)}&{\:\:\:\:\:{cos}\left(\theta\right)}\end{bmatrix} \\ $$$$ \\ $$$$\left.\mathrm{2}\right){solve} \\ $$$$ \\ $$$$\mathrm{6}{y}^{\mathrm{2}} {dx}−{x}\left({y}+\mathrm{2}{x}^{\mathrm{2}}…

prove-n-0-sinx-2n-sec-2-x-

Question Number 156795 by tabata last updated on 15/Oct/21 $${prove}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left({sinx}\right)^{\mathrm{2}{n}} ={sec}^{\mathrm{2}} {x}\:??? \\ $$ Answered by FongXD last updated on 15/Oct/21 $$\mathrm{we}\:\mathrm{have}:\:\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty}…