Question Number 211812 by mokys last updated on 21/Sep/24 $${prove}\:\underset{{x}\rightarrow\infty} {{lim}}\:\left(\:\mathrm{1}\:+\:\frac{\mathrm{5}}{{x}}\:\right)^{\frac{\mathrm{1}}{{x}}} −\:\mathrm{1}\:=\:\mathrm{5}\: \\ $$ Commented by mr W last updated on 22/Sep/24 $${wrong}! \\ $$$${the}\:{result}\:{should}\:{be}\:\mathrm{0}.…
Question Number 211796 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\sqrt{\frac{\mathrm{cos}\:\left({x}−{a}\right)}{\mathrm{sin}\:\left({x}+{a}\right)}}{dx}= \\ $$$$=\int\sqrt{\frac{\mathrm{cos}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{sin}\:{a}\:\mathrm{sin}\:{x}}{\mathrm{sin}\:{a}\:\mathrm{cos}\:{x}\:+\mathrm{cos}\:{a}\:\mathrm{sin}\:{x}}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\mathrm{tan}\:{x}\right] \\ $$$$=\int\sqrt{\frac{{t}\mathrm{sin}\:{a}\:+\mathrm{cos}\:{a}}{{t}\mathrm{cos}\:{a}\:+\mathrm{sin}\:{a}}}×\frac{{dt}}{{t}^{\mathrm{2}} +\mathrm{1}}= \\…
Question Number 211797 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 21/Sep/24 $$\int\frac{\sqrt{\mathrm{cot}\:{x}}−\sqrt{\mathrm{tan}\:{x}}}{\mathrm{1}+\mathrm{3sin}\:\mathrm{2}{x}}{dx}= \\ $$$$\:\:\:\:\:\left[{t}=\sqrt{\mathrm{tan}\:{x}}\right] \\ $$$$=−\mathrm{2}\int\frac{{t}^{\mathrm{2}} −\mathrm{1}}{{t}^{\mathrm{4}} +\mathrm{6}{t}^{\mathrm{2}} +\mathrm{1}}{dt}= \\…
Question Number 211798 by Spillover last updated on 21/Sep/24 Answered by Ghisom last updated on 22/Sep/24 $$\frac{\mathrm{e}^{\mathrm{cos}\:{x}} \left({x}\mathrm{sin}^{\mathrm{3}} \:{x}\:+\mathrm{cos}\:{x}\right)}{\mathrm{sin}^{\mathrm{2}} \:{x}}= \\ $$$$=\mathrm{e}^{\mathrm{cos}\:{x}} {x}\mathrm{sin}\:{x}\:+\frac{\mathrm{e}^{\mathrm{cos}\:{x}} \mathrm{cos}\:{x}}{\mathrm{sin}^{\mathrm{2}} \:{x}}=…
Question Number 211815 by alcohol last updated on 21/Sep/24 $${ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0}\:{has}\:{roots}\:\alpha\:{and}\:\beta \\ $$$${and}\:\frac{\alpha}{\beta}=\frac{\lambda}{\mu}.\:{show}\:{that}\:\lambda\mu{b}^{\mathrm{2}} \:=\:{ac}\left(\lambda+\mu\right)^{\mathrm{2}} \\ $$ Answered by som(math1967) last updated on 22/Sep/24 $$\:{let}\:\alpha={k}\lambda\:,\:\beta={k}\mu \\…
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Question Number 211791 by mathkun last updated on 20/Sep/24 $$\mathrm{can}\:\mathrm{someone}\:\mathrm{please}\:\mathrm{tell}\:\mathrm{me}\:\mathrm{the}\:\mathrm{difference}\:\mathrm{b}/\mathrm{w}\:\left(=\right)\:\mathrm{and}\:\left(::=\right) \\ $$$$ \\ $$$$\mathrm{I}\:\mathrm{searched}\:\mathrm{up}\:\mathrm{and}\:\mathrm{showed}\:\mathrm{it}\:\mathrm{was}\:\mathrm{related}\:\mathrm{to}\:\mathrm{assertion},\mathrm{definition},\mathrm{propert}\:\mathrm{def}….\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{know}.\:\mathrm{please}\:\mathrm{help} \\ $$ Answered by Frix last updated on 20/Sep/24 $${a}={b}\:\:\:\:\:{a}\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:{b} \\…
Question Number 211759 by liuxinnan last updated on 20/Sep/24 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{{e}^{\mathrm{sin}\:{x}} −{e}^{{x}} }{\mathrm{sin}\:{x}−{x}}=? \\ $$ Commented by liuxinnan last updated on 20/Sep/24 Answered by TonyCWX08…
Question Number 211787 by hardmath last updated on 20/Sep/24 $$\mathrm{Compare}: \\ $$$$ \\ $$$$\mathrm{5}^{\mathrm{100}} \:,\:\mathrm{6}^{\mathrm{91}} \:,\:\mathrm{7}^{\mathrm{90}} \:,\:\mathrm{8}^{\mathrm{85}} \\ $$ Terms of Service Privacy Policy Contact:…
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