Question Number 140530 by liberty last updated on 09/May/21 $$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)−\mathrm{ysec}\:\mathrm{y}}{\mathrm{x}}=? \\ $$ Answered by EDWIN88 last updated on 09/May/21 $$\:\mathrm{L}'\mathrm{H}\ddot {\mathrm{o}pital} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)+\left(\mathrm{x}+\mathrm{y}\right)\mathrm{sec}\:\left(\mathrm{x}+\mathrm{y}\right)\mathrm{tan}\:\left(\mathrm{x}+\mathrm{y}\right)−\mathrm{0}}{\mathrm{1}}…
Question Number 140525 by mathdanisur last updated on 09/May/21 $${x};{y};{z}>\mathrm{0}\:;\:{x}+{y}+{z}=\mathrm{3} \\ $$$${proof}\:\left({x}^{\mathrm{3}} +\mathrm{2}\right)\left({y}^{\mathrm{3}} +\mathrm{2}\right)\left({z}^{\mathrm{3}} +\mathrm{2}\right)\geqslant\mathrm{3}^{\mathrm{3}} \\ $$ Answered by mitica last updated on 09/May/21 $${jensen}…
Question Number 9455 by RasheedSoomro last updated on 09/Dec/16 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{following}\:\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$$\mathrm{3x}−\mathrm{8z}=−\mathrm{11} \\ $$$$\mathrm{2y}−\mathrm{3x}=−\mathrm{3} \\ $$$$\mathrm{y}−\mathrm{4z}=−\mathrm{7} \\ $$$${See}\:{the}\:{comment}\:{of}\:{Q}#\mathrm{9439}. \\ $$ Answered by geovane10math last updated…
Question Number 9453 by Raja Naik last updated on 09/Dec/16 $$\mathrm{find}\:\mathrm{dc}'\mathrm{s}\:\mathrm{dr}'\mathrm{s}\:\mathrm{of}\:\mathrm{a}\:\mathrm{mormal}\:\mathrm{to}\:\mathrm{the}\: \\ $$$$\mathrm{plane}\:\mathrm{2x}+\frac{\mathrm{5}}{\mathrm{2}}\mathrm{y}+\frac{\mathrm{7}}{\mathrm{8}}\mathrm{z}=\mathrm{23} \\ $$ Answered by mrW last updated on 10/Dec/16 $$\mathrm{d}.\mathrm{r}.'\mathrm{s}\:\mathrm{of}\:\mathrm{the}\:\mathrm{normal}\:\mathrm{are}\:\left(\mathrm{2},\frac{\mathrm{5}}{\mathrm{2}},\frac{\mathrm{7}}{\mathrm{8}}\right) \\ $$$$\sqrt{\mathrm{2}^{\mathrm{2}}…
Question Number 9449 by tawakalitu last updated on 08/Dec/16 $$\mathrm{2xy}\:=\:\mathrm{x}\:+\:\mathrm{y}\:\:\:\:\:……\:\left(\mathrm{i}\right) \\ $$$$\mathrm{6xz}\:=\:\mathrm{6z}\:−\:\mathrm{2x}\:\:\:\:…..\:\left(\mathrm{ii}\right) \\ $$$$\mathrm{3yz}\:=\:\mathrm{3y}\:+\:\mathrm{4z}\:\:\:…….\:\left(\mathrm{iii}\right) \\ $$$$ \\ $$$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$ Answered by mrW last updated…
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Question Number 74980 by ~blr237~ last updated on 05/Dec/19 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left[\mathrm{x}+\frac{\mathrm{p}}{\mathrm{n}}\right]=\left[\mathrm{nx}\right] \\ $$ Answered by mind is power last updated on 05/Dec/19…
Question Number 140513 by mathocean1 last updated on 08/May/21 $$\mathrm{n}\:\in\:\mathbb{N}^{\ast} \:\mathrm{and}\:\mathrm{k}\:\in\:\mathbb{N}^{\ast} . \\ $$$$\mathrm{Given}\:\mathrm{0}\leqslant\mathrm{k}\leqslant\mathrm{n}−\mathrm{1}. \\ $$$$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\frac{\mathrm{1}}{\mathrm{n}}\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}\right)\leqslant\underset{\mathrm{1}+\frac{\mathrm{k}}{\mathrm{n}}} {\overset{\mathrm{1}+\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}} {\int}}\mathrm{lnx}\:\mathrm{dn}\leqslant\frac{\mathrm{1}}{\mathrm{n}}\mathrm{ln}\left(\mathrm{1}+\frac{\mathrm{k}+\mathrm{1}}{\mathrm{n}}\right) \\ $$ Terms of Service…
Question Number 74978 by aliesam last updated on 05/Dec/19 Commented by aliesam last updated on 05/Dec/19 $${find}\:{the}\:{area}\:{of}\:{the}\:{red}\:{part} \\ $$ Answered by mind is power last…
Question Number 9439 by tawakalitu last updated on 08/Dec/16 $$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:,\:\mathrm{y}\:\mathrm{and}\:\mathrm{z} \\ $$$$\left(\mathrm{x}\:+\:\mathrm{1}\right)\left(\mathrm{y}\:+\:\mathrm{3}\right)\:=\:\mathrm{8}\:\:\:…….\:\left(\mathrm{i}\right) \\ $$$$\left(\mathrm{y}\:+\:\mathrm{3}\right)\left(\mathrm{z}\:−\:\mathrm{1}\right)\:=\:\mathrm{3}\:\:………\:\left(\mathrm{ii}\right) \\ $$$$\left(\mathrm{z}\:−\:\mathrm{1}\right)\left(\mathrm{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{2}\:\:\:………\:\left(\mathrm{iii}\right) \\ $$ Commented by RasheedSoomro last updated on 09/Dec/16…