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Author: Tinku Tara

let-f-x-0-1-arctan-1-xt-t-2-1-dt-determine-a-explicit-form-for-f-x-2-calculate-0-1-arctan-1-2t-1-t-2-dt-

Question Number 62437 by mathsolverby Abdo last updated on 21/Jun/19 $${let}\:{f}\left({x}\right)\:=\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctan}\left(\mathrm{1}+{xt}\right)}{{t}^{\mathrm{2}} \:+\mathrm{1}}{dt} \\ $$$${determine}\:{a}\:{explicit}\:{form}\:{for}\:{f}\left({x}\right) \\ $$$$\left.\mathrm{2}\right){calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{arctan}\left(\mathrm{1}+\mathrm{2}{t}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$$$ \\ $$…

You-have-given-a-positive-integer-N-Calculate-0-e-2pix-2-1-e-2pix-2-1-1-x-x-N-2-x-2-dx-

Question Number 127970 by Agnibhoo last updated on 03/Jan/21 $$\mathrm{You}\:\mathrm{have}\:\mathrm{given}\:\mathrm{a}\:\mathrm{positive}\:\mathrm{integer}\:{N}.\: \\ $$$$\mathrm{Calculate}\: \\ $$$$\int_{\:\mathrm{0}} ^{\:\infty} \frac{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:−\:\mathrm{1}}{{e}^{\mathrm{2}\pi{x}^{\mathrm{2}} } \:+\:\mathrm{1}}\left(\frac{\mathrm{1}}{{x}}\:−\:\frac{{x}}{{N}^{\mathrm{2}} \:−\:{x}^{\mathrm{2}} }\right)\:{dx} \\ $$ Answered…

let-f-x-ch-cosx-1-calculste-f-n-x-and-f-n-0-2-developp-f-at-integr-serie-

Question Number 62434 by mathsolverby Abdo last updated on 21/Jun/19 $${let}\:{f}\left({x}\right)={ch}\left({cosx}\right) \\ $$$$\left.\mathrm{1}\right){calculste}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Terms of Service Privacy Policy Contact:…

How-many-x-R-satisfy-x-1-7-x-1-5-x-1-3-x-

Question Number 127968 by liberty last updated on 03/Jan/21 $$\:\mathrm{How}\:\mathrm{many}\:\mathrm{x}\epsilon\mathbb{R}\:\mathrm{satisfy}\:\sqrt[{\mathrm{7}}]{\mathrm{x}}\:−\sqrt[{\mathrm{5}}]{\mathrm{x}}\:=\:\sqrt[{\mathrm{3}}]{\mathrm{x}}\:−\sqrt{\mathrm{x}}\: \\ $$ Answered by MJS_new last updated on 03/Jan/21 $${x}=\mathrm{0}\vee{x}\approx.\mathrm{0117154773}\vee{x}=\mathrm{1} \\ $$ Terms of Service…

Question-62431

Question Number 62431 by rajesh4661kumar@gamil.com last updated on 21/Jun/19 Answered by tanmay last updated on 21/Jun/19 $${asin}^{\mathrm{2}} \theta+{bcos}^{\mathrm{2}} \theta={c} \\ $$$${asin}^{\mathrm{2}} \theta+{b}\left(\mathrm{1}−{sin}^{\mathrm{2}} \theta\right)={c} \\ $$$${sin}^{\mathrm{2}}…

let-x-n-1-1-n-x-with-x-gt-1-1-calculate-lim-x-1-x-and-lim-x-x-2-prove-that-x-1-2-x-o-2-x-x-3-prove-that-is-decreasing-and-convexe-fuc

Question Number 62425 by mathmax by abdo last updated on 21/Jun/19 $${let}\:\xi\left({x}\right)\:=\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{{x}} }\:\:\:\:\:{with}\:{x}>\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{lim}_{{x}\rightarrow\mathrm{1}^{+} } \:\:\xi\left({x}\right)\:\:{and}\:{lim}_{{x}\rightarrow+\infty} \:\:\:\xi\left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\xi\left({x}\right)\:=\mathrm{1}+\mathrm{2}^{−{x}} \:+{o}\left(\mathrm{2}^{−{x}} \right)\:\:\:\left({x}\rightarrow+\infty\right) \\…