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Question Number 127481 by Mathgreat last updated on 30/Dec/20 Commented by hknkrc46 last updated on 30/Dec/20 $${g}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:\mathrm{1}\:\Rightarrow\:{g}^{−\mathrm{1}} \left({x}\right)\:=\:\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}} \\ $$$${f}\left({x}^{\mathrm{3}} \:+\:\mathrm{1}\right)\mid_{\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}}} \:=\:\left({x}^{\mathrm{5}} \:+\:\mathrm{4}{x}\:+\:\mathrm{2}\right)\mid_{\sqrt[{\mathrm{3}}]{{x}\:−\:\mathrm{1}}} \\…
Question Number 127477 by ZiYangLee last updated on 30/Dec/20 $$\mathrm{If}\:{y}=\frac{\mathrm{1}}{{x}\left(\mathrm{1}−{x}\right)}, \\ $$$$\mathrm{show}\:\mathrm{that}\:\frac{{d}^{{n}} {y}}{{dx}^{{n}} }={n}!\left[\frac{\left(−\mathrm{1}\right)^{{n}} }{{x}^{{n}+\mathrm{1}} }+\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{{n}+\mathrm{1}} }\right] \\ $$ Answered by Dwaipayan Shikari last updated…
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Question Number 61937 by Tawa1 last updated on 12/Jun/19 $$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\:\:\underset{\mathrm{n}\:=\:\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{n}^{\mathrm{3}} \:+\:\mathrm{5}}{\mathrm{n}!} \\ $$ Commented by mr W last updated on 12/Jun/19 $${seems}\:{to}\:{be}\:\mathrm{10}{e}. \\…
Question Number 61934 by Cypher1207 last updated on 12/Jun/19 $$\mathrm{Answer}:\:\mathrm{0}^{\mathrm{0}} =? \\ $$ Commented by Kunal12588 last updated on 12/Jun/19 $$\mathrm{I}\:\mathrm{believe}\:\mathrm{0}^{\mathrm{0}} =\mathrm{1} \\ $$ Commented…
Question Number 127468 by bramlexs22 last updated on 30/Dec/20 $$\:\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{x}^{\mathrm{3}} \:\mathrm{sin}\:\left(\lambda\mathrm{x}\right)}{\mathrm{x}^{\mathrm{4}} +\mathrm{4}}\:\mathrm{dx}\:=?\: \\ $$ Commented by bramlexs22 last updated on 30/Dec/20 $$\mathrm{thank}\:\mathrm{you}\:\mathrm{both}\:\mathrm{sir} \\…
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Question Number 192999 by Mastermind last updated on 01/Jun/23 $$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{following}\:\mathrm{functions} \\ $$$$\mathrm{are}\:\mathrm{continous}\:\mathrm{on}\:\mathrm{a}\:\mathrm{close}\:\mathrm{interval} \\ $$$$\left[\mathrm{0},\:\mathrm{1}\right]. \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\left\{_{\mathrm{3}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}=\mathrm{1}} ^{\frac{\mathrm{x}^{\mathrm{2}} +\mathrm{x}−\mathrm{2}}{\mathrm{x}−\mathrm{1}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}\neq\mathrm{1}} \right. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$…