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1-lim-x-0-sin-1-x-2-lim-x-0-cos-1-x-

Question Number 110647 by Khalmohmmad last updated on 29/Aug/20 $$\left.\:\mathrm{1}\right)\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}sin}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=? \\ $$$$\left.\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}cos}\:\left(\frac{\mathrm{1}}{\mathrm{x}}\right)=? \\ $$$$ \\ $$ Answered by mathmax by abdo last updated…

a-b-c-R-and-abc-1-Prove-c-a-3-b-3-a-2-b-2-b-a-3-c-3-a-2-c-2-a-b-3-c-3-b-2-c-2-3-2-

Question Number 176174 by Matica last updated on 14/Sep/22 $$ \\ $$$$\:\mathrm{a},{b},{c}\:\in\mathbb{R}_{+\:} ^{\ast} \:\:\mathrm{and}\:{abc}=\mathrm{1}.\:\mathrm{Prove} \\ $$$$\:\:\:\frac{{c}\:\sqrt{{a}^{\mathrm{3}} +{b}^{\mathrm{3}} }}{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} }\:+\:\frac{{b}\:\sqrt{{a}^{\mathrm{3}} +{c}^{\mathrm{3}} }}{{a}^{\mathrm{2}} +{c}^{\mathrm{2}} }\:+\:\frac{{a}\sqrt{{b}^{\mathrm{3}} +{c}^{\mathrm{3}}…

someone-posted-this-problem-and-my-solution-followed-solve-0-1-ln-x-1-x-2-1-x-2-dx-solution-y-ln-x-1-x-2-and-dy-1-1-x-2-dx-at-x-0-y-0-and-at-x-1-y-ln-1-2-hen

Question Number 110619 by mathdave last updated on 29/Aug/20 $${someone}\:{posted}\:{this}\:{problem}\:{and}\:{my} \\ $$$${solution}\:{followed} \\ $$$${solve} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$$${solution} \\ $$$${y}=\mathrm{ln}\left({x}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right)\:\:\:{and}\:\:{dy}=\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}^{\mathrm{2}}…

Question-110614

Question Number 110614 by mathdave last updated on 29/Aug/20 Answered by Dwaipayan Shikari last updated on 29/Aug/20 $$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\left({cosx}\right)^{\pi} }{\left({cosx}\right)^{\pi} +\left({sinx}\right)^{\pi} }{dx}=\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\left({sinx}\right)^{\pi}…

Prove-that-4n-lt-2-n-for-all-n-5-

Question Number 176102 by MathsFan last updated on 12/Sep/22 $$\:\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\: \\ $$$$\:\:\:\:\:\mathrm{4}\boldsymbol{\mathrm{n}}<\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{all}}\:\boldsymbol{\mathrm{n}}\geqslant\mathrm{5} \\ $$ Answered by a.lgnaoui last updated on 12/Sep/22 $${n}=\mathrm{5}\:\:\:\mathrm{2}^{\mathrm{5}} =\mathrm{32}\:\:\:\:\:\:\:\:\:\mathrm{4}×\mathrm{5}=\mathrm{20}<\mathrm{32} \\…

it-seems-too-hard-for-many-here-to-post-their-questions-as-questions-answers-as-answers-and-comments-as-comments-hereby-I-introduce-the-next-step-I-ll-post-answers-and-the-task-is-find-questions

Question Number 110539 by Her_Majesty last updated on 29/Aug/20 $${it}\:{seems}\:{too}\:{hard}\:{for}\:{many}\:{here}\:{to}\:{post} \\ $$$${their}\:{questions}\:{as}\:{questions},\:{answers}\:{as} \\ $$$${answers}\:{and}\:{comments}\:{as}\:{comments}… \\ $$$${hereby}\:{I}\:{introduce}\:{the}\:{next}\:{step}:\:{I}'{ll}\:{post} \\ $$$${answers}\:{and}\:{the}\:{task}\:{is},\:{find}\:{questions} \\ $$$${to}\:{these}\:{answers} \\ $$$$\left(\mathrm{1}\right)\:\zeta\left(\mathrm{3}\right)+\pi{ln}\mathrm{2} \\ $$$$\left(\mathrm{2}\right)\:\pi{H}_{\mathrm{0}} \left(\mathrm{7}\right)…