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Question Number 61791 by naka3546 last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty} {\mathrm{lim}}\:\:\:\frac{\mathrm{6}^{{x}} }{\mathrm{2}^{{x}} \:+\:\mathrm{4}^{{x}} }\:\:\:=\:\:\:\infty\:\:\:\:\:? \\ $$ Commented by mr W last updated on 08/Jun/19 $$\underset{{x}\:\rightarrow\:\infty}…
Question Number 127322 by MathSh last updated on 28/Dec/20 $${f}\left({x}\right)\:{function}\:{pair}\:{and}\:\left(−\infty;\mathrm{0}\right] \\ $$$${decreases}\:{in}\:{the}\:{range} \\ $$$${f}\left({x}\right)\geqslant{f}\left(−\mathrm{3}\right)\:{solve}\:{the}\:{inequality} \\ $$ Answered by mindispower last updated on 28/Dec/20 $$\left.\right]\left.−\infty,−\mathrm{3}\right]\cup\left[\mathrm{3},+\infty\left[\right.\right. \\…
Question Number 192858 by josemate19 last updated on 29/May/23 $$\int_{\mathrm{4}{x}} ^{\:{x}^{\mathrm{3}} } \sqrt{\sqrt{{t}}+{t}^{\mathrm{1}/\mathrm{3}} }{dt} \\ $$ Answered by Frix last updated on 29/May/23 $$\int\sqrt{\sqrt{{t}}+\sqrt[{\mathrm{3}}]{{t}}}{dt}= \\…
Question Number 61782 by naka3546 last updated on 08/Jun/19 $${Any}\:\:{integer}\left({s}\right)\:\:{which}\:\:{fulfill} \\ $$$$\:\:\:\:\:\:\:\:\:\:{n}^{\mathrm{5}} \:−\:\mathrm{5}{n}^{\mathrm{3}} \:+\:\mathrm{5}{n}\:+\:\mathrm{1}\:\:\mid\:\:{n}!\:\:\:? \\ $$ Commented by naka3546 last updated on 08/Jun/19 $${please}\:\:{show}\:\:{workings}\:! \\…
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Question Number 61778 by naka3546 last updated on 08/Jun/19 $${Any}\:\:{integer}\left({s}\right)\:\:{which}\:\:{fulfill}\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{n}^{\mathrm{3}} \:−\:\mathrm{5}{n}^{\mathrm{2}} \:+\:\mathrm{5}{n}\:+\:\mathrm{1}\:\:\mid\:\:{n}!\:\:\:\:? \\ $$ Answered by MJS last updated on 08/Jun/19 $$\frac{{n}!}{{n}^{\mathrm{3}} −\mathrm{5}{n}^{\mathrm{2}}…
Question Number 127305 by MathSh last updated on 28/Dec/20 $$\left({a}−\mathrm{3}\right)^{−\frac{\mathrm{1}}{\mathrm{5}}} \\ $$$${the}\:{set}\:{of}\:{possible}\:{values}\:{of}\:{a} \\ $$$$\left.{a}\right)\left(−\infty;+\infty\right) \\ $$$$\left.{b}\right)\left(\mathrm{3};+\infty\right) \\ $$$$\left.{e}\right){a}\neq\mathrm{3} \\ $$ Answered by MJS_new last updated…
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