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Category: Differentiation

Find-the-cordinates-of-the-two-points-on-the-curve-y-4-x-2-whose-tangents-pass-through-the-point-1-7-

Question Number 5614 by Rasheed Soomro last updated on 22/May/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cordinates}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{points} \\ $$$$\mathrm{on}\:\mathrm{the}\:\mathrm{curve}\:\mathrm{y}=\mathrm{4}−\mathrm{x}^{\mathrm{2}} \:\:\mathrm{whose}\:\mathrm{tangents} \\ $$$$\mathrm{pass}\:\mathrm{through}\:\mathrm{the}\:\mathrm{point}\:\left(−\mathrm{1},\:\mathrm{7}\right)\:. \\ $$ Commented by Rasheed Soomro last updated on…

The-tangent-at-the-point-P-a-b-on-the-curve-y-ab-x-meets-the-x-axis-and-y-axis-at-Q-and-R-respectively-Show-that-PQ-RP-

Question Number 5615 by Rasheed Soomro last updated on 22/May/16 $$\mathrm{The}\:\mathrm{tangent}\:\mathrm{at}\:\mathrm{the}\:\mathrm{point}\:\mathrm{P}\left({a},{b}\right)\:\mathrm{on}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\:\mathrm{y}=\frac{{ab}}{{x}}\:\:\mathrm{meets}\:\mathrm{the}\:\mathrm{x}-\mathrm{axis}\:\mathrm{and}\:\mathrm{y}-\mathrm{axis} \\ $$$$\mathrm{at}\:\mathrm{Q}\:\mathrm{and}\:\mathrm{R}\:\mathrm{respectively}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{PQ}=\mathrm{RP}\:. \\ $$ Commented by prakash jain last updated…

Im-C-0-1-2-z-dz-pi-2-

Question Number 136682 by snipers237 last updated on 24/Mar/21 $$\:{Im}\left(\int_{{C}^{+} \left(\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)} \overset{−} {{z}dz}\:\right)=\:\frac{\pi}{\mathrm{2}}\:\: \\ $$ Answered by Olaf last updated on 24/Mar/21 $$\Omega\:=\:\mathrm{Im}\int_{\mathrm{C}^{+} \left(\mathrm{0},\frac{\mathrm{1}}{\mathrm{2}}\right)} \overset{−}…

If-n-gt-1-prove-by-mathematical-induction-that-n-n-1-1-n-1-lt-1-1-2-1-3-1-4-1-n-

Question Number 5513 by 314159 last updated on 17/May/16 $${If}\:{n}>\mathrm{1},\:{prove}\:{by}\:{mathematical}\:{induction}\:{that} \\ $$$${n}\left(\left({n}+\mathrm{1}\right)^{\frac{\mathrm{1}}{{n}}} −\mathrm{1}\right)\:<\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+…\frac{\mathrm{1}}{{n}}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

advanced-calculus-pove-that-n-0-1-n-2-2n-2n-n-cos-nx-cos-x-4-2cos-x-2-

Question Number 136581 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:…….{advanced}\:\:\:{calculus}…. \\ $$$$\:\:\:{pove}\:{that}:: \\ $$$$:::\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left\{\frac{\left(−\mathrm{1}\right)^{{n}} }{\mathrm{2}^{\mathrm{2}{n}} }\begin{pmatrix}{\:\mathrm{2}{n}}\\{\:\:{n}}\end{pmatrix}\:{cos}\left({nx}\right)\right\}=\frac{{cos}\left(\frac{{x}}{\mathrm{4}}\right)}{\:\sqrt{\mathrm{2}{cos}\left(\frac{{x}}{\mathrm{2}}\right)}} \\ $$ Answered by Dwaipayan Shikari last…

nice-calculus-n-0-cos-n-x-cos-nx-solution-1-2-n-0-cos-n-1-x-cos-x-nx-cos-x-nx-2-n-0-cos-n-1-x-cos-n-1-x-

Question Number 136570 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:…….{nice}\:\:…..\:\:\:{calculus}….. \\ $$$$\:\:\:\:\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}} \left({x}\right).{cos}\left({nx}\right)=? \\ $$$$\:\:\:{solution}:::: \\ $$$$\:\:\:\:\Omega=\frac{\mathrm{1}}{\mathrm{2}}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{cos}^{{n}−\mathrm{1}} \left({x}\right)\left\{{cos}\left({x}−{nx}\right)+{cos}\left({x}+{nx}\right)\right. \\ $$$$\:\:\therefore\:\mathrm{2}\Omega=\underset{{n}=\mathrm{0}} {\overset{\infty}…

nice-calculus-prove-that-0-ln-1-x-2-1-x-2-2-dx-pi-2-ln-2-pi-4-

Question Number 136555 by mnjuly1970 last updated on 23/Mar/21 $$\:\:\:\:\:\:\:\:\:….{nice}\:\:\:\:……\:\:\:{calculus}…. \\ $$$$\:\:\:{prove}\:{that} \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\phi}=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}=\frac{\pi}{\mathrm{2}}{ln}\left(\mathrm{2}\right)−\frac{\pi}{\mathrm{4}} \\ $$$$\:\:\:\:\::::::::: \\ $$ Answered by…