Question Number 137650 by bemath last updated on 05/Apr/21 Answered by bemath last updated on 05/Apr/21 $${By}\:{Langrange}\:{multiplier} \\ $$$${f}\left({x},{y},\lambda\right)=\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +\lambda\left(\mathrm{6}{x}^{\mathrm{2}} +\mathrm{2}{xy}+\mathrm{6}{y}^{\mathrm{2}} −\mathrm{9}\right) \\ $$$$\frac{\partial{f}}{\partial{x}}\:=\:\mathrm{2}{x}+\lambda\left(\mathrm{12}{x}+\mathrm{2}{y}\right)=\mathrm{0}…
Question Number 137597 by bemath last updated on 04/Apr/21 $$ \\ $$Find the minimum value of x^(2) +y^(2) +z^(2) , subject to the condition 2x+3y+5z=30?…
Question Number 72044 by 20190927 last updated on 23/Oct/19 $$\mathrm{y}=\mathrm{ln}\left(\mathrm{3x}^{\mathrm{2}} +\mathrm{x}\right)\:\:\:\mathrm{solve}\:\mathrm{y}^{\left(\mathrm{6}\right)} \left(\mathrm{x}\right) \\ $$ Commented by mathmax by abdo last updated on 24/Oct/19 $${we}\:{have}\:{y}^{'} \left({x}\right)=\frac{\mathrm{6}{x}+\mathrm{1}}{\mathrm{3}{x}^{\mathrm{2}}…
Question Number 137378 by benjo_mathlover last updated on 02/Apr/21 $${Given}\:\underset{\mathrm{0}} {\int}^{\:{x}} {f}\left({t}\right)\:{dt}\:=\:{x}^{\mathrm{2}} \:\mathrm{sin}\:\left(\pi{x}\right) \\ $$$${find}\:{f}\left(\mathrm{2}\right). \\ $$ Answered by EDWIN88 last updated on 02/Apr/21 $$\:\frac{\mathrm{d}}{\mathrm{dx}}\:\left[\:\int_{\mathrm{0}}…
Question Number 6233 by sanusihammed last updated on 19/Jun/16 $${Diffrentiate}\:\:\:\:{y}\:\:=\:\:{x}^{\mathrm{3}{ln}\mathrm{5}} \\ $$ Answered by malwaan last updated on 19/Jun/16 $${y}^{'} =\mathrm{3}{ln}\mathrm{5}{x}^{\mathrm{3}{ln}\mathrm{5}−\mathrm{1}} \\ $$ Answered by…
Question Number 71769 by psyche last updated on 19/Oct/19 $${show}\:{that}\:{if}\:{f}\:{is}\:{a}\:{differentiable}\:{function}\:{at}\:{the}\:{point}\:{x}={a},\:{then}\:{f}\:{is}\:{continuous}\:{at}\:{x}={a}. \\ $$ Commented by kaivan.ahmadi last updated on 19/Oct/19 $${if}\:{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)\neq{f}\left({a}\right)\:\Rightarrow{lim}_{{x}\rightarrow{a}} {f}\left({x}\right)−{f}\left({a}\right)\neq\mathrm{0}\Rightarrow \\ $$$${then}\:{f}'\left({a}\right)={lim}_{{x}\rightarrow{a}} \frac{{f}\left({x}\right)−{f}\left({a}\right)}{{x}−{a}}=+\infty\vee−\infty…
Question Number 137303 by Raxreedoroid last updated on 31/Mar/21 $$\mathrm{from}\:\mathrm{the}\:\mathrm{figure}\:\mathrm{above} \\ $$$${the}\:{square}\:{S}'\mathrm{s}\:\mathrm{diameter}\:\mathrm{length}\:\mathrm{is}\:\mathrm{increasing} \\ $$$$\mathrm{by}\:\mathrm{25}\:\mathrm{m}/\mathrm{s}\:\mathrm{to}\:\mathrm{the}\:\mathrm{north}−\mathrm{east}\:\mathrm{initially}\:\mathrm{at}\:\mathrm{length}\:\mathrm{30}\sqrt{\mathrm{2}\:}\mathrm{m}\:\mathrm{and}\:\mathrm{circle}\: \\ $$$${C}'\mathrm{s}\:\mathrm{radius}\:\mathrm{is}\:\mathrm{decreasing}\:\mathrm{by}\:\mathrm{2}\:\mathrm{m}/\mathrm{s}\:\mathrm{initially}\:\mathrm{at}\:\mathrm{length}\:\mathrm{100}\:\mathrm{m} \\ $$$$\mathrm{knowing}\:\mathrm{that}\:\mathrm{the}\:\mathrm{blue}\:\mathrm{line}'\mathrm{s}\:\mathrm{length}\:=\:\mathrm{40m} \\ $$$$\mathrm{at}\:\mathrm{what}\:\mathrm{time}\:\mathrm{the}\:\mathrm{horizontal}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{point}\:{p} \\ $$$$\mathrm{and}\:\mathrm{point}\:{q}\:\mathrm{will}\:\mathrm{equal}\:\mathrm{0}? \\ $$$$\mathrm{and}\:\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{the}\:\mathrm{vertical}\:\mathrm{distance}\:\mathrm{at}\:\mathrm{that}\:\mathrm{time}? \\…
Question Number 137275 by mnjuly1970 last updated on 31/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:……{complex}\:\:{analysis}….. \\ $$$$\:\:\:\:{if}\:,\:\:{f}\left(\alpha,{n},{x}\right)=\frac{{d}^{\:{n}} }{{dx}^{{n}} }\left(\alpha^{{x}} \right)\:\:,\:{x}\in\mathbb{C} \\ $$$$\:\:\:\:\:\alpha\in\mathbb{C}−\left\{\mathrm{0}\right\}\:,\:{n}\in\mathbb{C}−\mathbb{Z}^{−} \cup\left\{\mathrm{0}\right\} \\ $$$$\:\:\:\:\:{and}\:\:{g}\left({n},{x}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} {f}\left(\alpha,{n},{x}\right){d}\alpha \\ $$$$\:\:\:\:\:{then}\:\:{find}\:\:{the}\:{value}\:{of}\:… \\…
Question Number 6180 by FilupSmith last updated on 17/Jun/16 $$\frac{{df}\left({x}\right)}{{dx}}={f}\left({x}\right)+{x} \\ $$$$\mathrm{Solve}\:{f}\left({x}\right) \\ $$ Commented by 123456 last updated on 17/Jun/16 $$\frac{{df}}{{dx}}−{f}={x} \\ $$$${f}={f}_{{n}} +{f}_{{g}}…
Question Number 137249 by bemath last updated on 31/Mar/21 $$\int\:\frac{\left(\mathrm{3sin}\:\mathrm{x}+\mathrm{2}\right)}{\left(\mathrm{2sin}\:\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} }\:\mathrm{dx}\:=? \\ $$ Answered by bemath last updated on 31/Mar/21 $$\mathrm{let}\:\mathrm{tan}\:\left(\frac{\mathrm{x}}{\mathrm{2}}\right)=\mathrm{u}\: \begin{cases}{\mathrm{dx}=\frac{\mathrm{2}}{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{du}}\\{\mathrm{sin}\:\mathrm{x}=\frac{\mathrm{2u}}{\mathrm{u}^{\mathrm{2}} +\mathrm{1}}}\end{cases} \\…