Question Number 24764 by NECx last updated on 25/Nov/17 $${Given}\:{that}\:{the}\:{function}\:{f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${is}\:{defined}\:{by}\:{f}\left({x}\right)={x}^{{n}} .{For}\:{what} \\ $$$${values}\:{of}\:{n},{if}\:{any},{is}\:{fof}={f}.{f}? \\ $$$${For}\:{each}\:{of}\:{these}\:{values}\:{of}\:{n}\:{find} \\ $$$${fof}. \\ $$ Answered by mrW1 last…
Question Number 90299 by zainal tanjung last updated on 22/Apr/20 $$\mathrm{help}\:\mathrm{me} \\ $$$$ \\ $$$$\mathrm{z}\left(\mathrm{x},\mathrm{y}\right)=\mathrm{xy}.\mathrm{ln}\:\mathrm{xy} \\ $$$$\mathrm{z}_{\mathrm{x}} ^{'} =…?\:\:\:\mathrm{and}\:\:\mathrm{z}'_{\mathrm{y}} =…? \\ $$ Terms of Service…
Question Number 155829 by zainaltanjung last updated on 05/Oct/21 $$\mathrm{Find}\:\mathrm{this}\:\mathrm{excercise}\:\mathrm{about}\:\mathrm{limits} \\ $$$$\mathrm{trigonometri} \\ $$$$\left.\mathrm{1}\right).\:\underset{\theta\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{2cos}\:\theta−\mathrm{2}}{\mathrm{3}\theta} \\ $$$$\left.\mathrm{2}\right).\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mathrm{cos}\:\mathrm{x}}{\mathrm{x}^{\frac{\mathrm{2}}{\mathrm{3}}} } \\ $$$$\left.\mathrm{3}\right).\:\underset{\mathrm{t}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{4t}^{\mathrm{2}} +\mathrm{3t}\:\mathrm{sin}\:\mathrm{t}}{\mathrm{t}^{\mathrm{2}} } \\…
Question Number 90292 by mathmax by abdo last updated on 22/Apr/20 $${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{e}^{{zx}^{\mathrm{2}} } }{{x}^{\mathrm{2}} }{dx}\:{with}\:{z}\:{from}\:{C}\:{and}\:{Re}\left({z}\right)<\mathrm{0} \\ $$ Commented by mathmax by abdo last…
Question Number 24755 by Anoop kumar last updated on 25/Nov/17 $${Given} \\ $$$${f}\left({x}\right)\:=\underset{{x}=\mathrm{1}} {\overset{{n}} {\sum}}{tan}\left(\frac{{x}}{\mathrm{2}^{{r}} }\right).{sec}\left(\frac{{x}}{\mathrm{2}^{{r}−\mathrm{1}} }\right)\: \\ $$$$\:\:\:\:\:\:\:\:\:{where}\:{r}\:{and}\:{n}\:\varepsilon{N} \\ $$$${g}\left({x}\right)\:=\underset{{n}\rightarrow\propto} {\mathrm{li}{m}}\:\:\frac{{ln}\left({f}\left({x}\right)+{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right)\:−\left({f}\left({x}\right)+{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right).\left[{sin}\left({tan}\frac{{x}}{\mathrm{2}}\right)\right.}{\mathrm{1}+\left({f}\left({x}\right)\:\:+\:\:{tan}\frac{{x}}{\mathrm{2}^{{n}} }\right)^{{n}}…
Question Number 90291 by mathmax by abdo last updated on 22/Apr/20 $${calculste}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}−{e}^{{zx}} }{{x}}{dx}\:\:{with}\:{z}\:{from}\:{C}\:{and}\:{Re}\left({z}\right)>\mathrm{0} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 24753 by math solver last updated on 25/Nov/17 Answered by iv@0uja last updated on 27/Nov/17 $$\left[\mathrm{11111}=\mathrm{41}×\mathrm{271}\right] \\ $$$${a}_{\mathrm{124}} =\mathrm{1111}+\mathrm{10}^{\mathrm{4}} ×\mathrm{11111}+\mathrm{10}^{\mathrm{9}} ×\mathrm{11111}+… \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…+\mathrm{10}^{\mathrm{114}}…
Question Number 90287 by jagoll last updated on 22/Apr/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{6}\:,\:\mathrm{x}\geqslant\mathrm{1}}\\{\mathrm{x}^{\mathrm{4}} +\mathrm{2x}^{\mathrm{3}} +\mathrm{2}\:,\mathrm{x}<\mathrm{1}}\end{cases} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{there}\:\mathrm{is}\:\mathrm{a}\:\mathrm{number}\: \\ $$$$\mathrm{c}\:\in\:\left(−\mathrm{2},\mathrm{3}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{f}\left(\mathrm{c}\right)\:=\:\mathrm{4} \\ $$ Answered by MJS last updated on…
Question Number 90282 by 20000193 last updated on 22/Apr/20 $$\frac{\mathrm{1}}{\mathrm{2}\alpha+\beta}+\frac{\mathrm{1}}{\alpha+\mathrm{2}\beta} \\ $$ Commented by jagoll last updated on 22/Apr/20 $$\frac{\alpha+\mathrm{2}\beta+\mathrm{2}\alpha+\beta}{\left(\mathrm{2}\alpha+\beta\right)\left(\alpha+\mathrm{2}\beta\right)}\:=\:\frac{\mathrm{3}\alpha+\mathrm{3}\beta}{\mathrm{2}\alpha^{\mathrm{2}} +\mathrm{5}\alpha\beta+\mathrm{2}\beta^{\mathrm{2}} } \\ $$ Terms…
Question Number 24747 by NECx last updated on 25/Nov/17 $${if}\:{f}\left({x}\right)=\mathrm{2}\mid{x}−\mathrm{3}\mid\:{and}\:{g}\left({x}\right)={x}^{\mathrm{2}} .{Find}: \\ $$$$\left({i}\right){gof}\:\left({ii}\right){fog}\:\left({iii}\right){domain}\:{of}\:{fog} \\ $$$$\left({iv}\right){range}\:{of}\:{gof} \\ $$$$ \\ $$ Answered by ajfour last updated on…