Question Number 42808 by maxmathsup by imad last updated on 02/Sep/18 $${let}\:{f}\left({x}\right)\:=\:\int_{{x}} ^{\mathrm{2}{x}} \:\:\frac{\mathrm{1}+{cos}\left({t}\right)}{\:\sqrt{{t}^{\mathrm{4}} −{t}^{\mathrm{2}} \:+\mathrm{4}}}{dt} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{D}_{{f}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:{f}^{'} \left({x}\right) \\ $$$$\left.\mathrm{3}\right)\:{find}\:{lim}_{{x}\rightarrow+\infty} \:{f}\left({x}\right) \\…
Question Number 173836 by mathlove last updated on 19/Jul/22 Commented by aleks041103 last updated on 21/Jul/22 $${I}=\int_{−\mathrm{2}} ^{−\mathrm{1}} \left(\mathrm{10}\sqrt[{\mathrm{4}}]{{x}^{\mathrm{6}} }−\mathrm{2}{x}\right){dx}= \\ $$$$=\mathrm{10}\int_{−\mathrm{2}} ^{−\mathrm{1}} \sqrt[{\mathrm{4}}]{{x}^{\mathrm{6}} }{dx}\:−\:\int_{−\mathrm{2}}…
Question Number 108208 by bemath last updated on 15/Aug/20 $$\:\:\:\:\:\:\:\frac{\mathcal{B}{e}\mathcal{M}{ath}}{\boxminus} \\ $$$$\left(\mathrm{1}\right)\int\:\frac{{x}^{\mathrm{5}} −{x}}{{x}^{\mathrm{8}} +\mathrm{1}}\:{dx}\: \\ $$$$\left(\mathrm{2}\right)\:\underset{\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}} {\overset{\mathrm{1}} {\int}}\:\frac{\mathrm{sin}^{−\mathrm{1}} \left({x}\right)}{{x}^{\mathrm{3}} }\:{dx}\: \\ $$ Answered by john…
Question Number 42538 by ajfour last updated on 27/Aug/18 Commented by ajfour last updated on 29/Aug/18 $${Q}.\mathrm{42446}\:\:\:{Find}\:\boldsymbol{{r}}_{\boldsymbol{{max}}} {if}\:{radius}\:{of} \\ $$$${larger}\:{circle}\:{is}\:{R}. \\ $$ Answered by ajfour…
Question Number 42448 by Tawa1 last updated on 25/Aug/18 Answered by tanmay.chaudhury50@gmail.com last updated on 25/Aug/18 $${y}=\sqrt{\mathrm{3}{x}^{\mathrm{2}} .{y}} \\ $$$${y}=\mathrm{3}{x}^{\mathrm{2}} \\ $$$$\frac{{dy}}{{dx}}=\mathrm{6}{x} \\ $$ Commented…
Question Number 42446 by ajfour last updated on 25/Aug/18 Commented by ajfour last updated on 26/Aug/18 $${Find}\:{maximum}\:\boldsymbol{{r}}\:{in}\:{terms}\:{of} \\ $$$$\boldsymbol{{a}}\:{and}\:\boldsymbol{{R}}.\: \\ $$ Answered by tanmay.chaudhury50@gmail.com last…
Question Number 107923 by bemath last updated on 13/Aug/20 $$\:\:\:\:\:\frac{\circledcirc\mathbb{B}{e}\mathcal{M}{ath}\circledcirc}{} \\ $$$$\:\:\:\:\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:{x}^{\frac{\mathrm{9}}{\mathrm{2}}} \:\left(\mathrm{1}−{x}\right)^{\frac{\mathrm{5}}{\mathrm{2}}} \:{dx}\:? \\ $$ Answered by 1549442205PVT last updated on 13/Aug/20…
Question Number 107810 by mnjuly1970 last updated on 12/Aug/20 Answered by hgrocks last updated on 12/Aug/20 Commented by mnjuly1970 last updated on 15/Aug/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{so}\:\mathrm{much}\:\mathrm{sir}. \\…
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Question Number 107658 by john santu last updated on 12/Aug/20 $$\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$${A}\:{metal}\:{box}\:\left({without}\:{top}\right)\:{is}\:{tobe} \\ $$$${contructed}\:{from}\:{a}\:{square}\:{sheet} \\ $$$${of}\:{metal}\:{that}\:{is}\:\mathrm{10}\:{dm}\:{on}\:{the} \\ $$$${side}\:{by}\:{first}\:{cutting}\:{the}\:{square} \\ $$$${pieces}\:{of}\:{the}\:{same}\:{size}\:{from}\:{the} \\ $$$${corners}\:{of}\:{the}\:{sheet}\:{and}\:{folding} \\ $$$${up}\:{sides}.\:{what}\:{size}\:{squares}…