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Author: Tinku Tara

an-object-is-placed-5cm-away-from-a-plane-mirror-the-mirror-is-rotated-tbrough-angle-20-0-about-the-point-of-incidence-calculate-the-shortest-distance-between-the-old-and-the-new-position-of-the-im

Question Number 133115 by aurpeyz last updated on 19/Feb/21 $${an}\:{object}\:{is}\:{placed}\:\mathrm{5}{cm}\:{away}\:{from}\:{a} \\ $$$${plane}\:{mirror}.\:{the}\:{mirror}\:{is}\:{rotated} \\ $$$${tbrough}\:{angle}\:\mathrm{20}^{\mathrm{0}} \:{about}\:{the}\:{point}\:{of} \\ $$$${incidence}.\:{calculate}\:{the}\:{shortest} \\ $$$${distance}\:{between}\:{the}\:{old}\:{and}\:{the}\:{new} \\ $$$${position}\:{of}\:{the}\:{image} \\ $$ Answered by…

lim-x-x-2-x-x-1-4-sin-2-x-x-2-sin-3x-

Question Number 133114 by bemath last updated on 19/Feb/21 $$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\left(\frac{\sqrt{\mathrm{x}^{\mathrm{2}} −\mathrm{x}}}{\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\mathrm{sin}\:\left(\frac{\mathrm{2}}{\mathrm{x}}\right)\right)^{\mathrm{x}^{\mathrm{2}} +\mathrm{sin}\:\mathrm{3x}} ? \\ $$ Answered by bobhans last updated on 19/Feb/21 $${L}=\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\sqrt{{x}^{\mathrm{2}}…

dx-x-4-1-x-4-2-1-4-

Question Number 133109 by EDWIN88 last updated on 18/Feb/21 $$\int\:\frac{{dx}}{\left({x}^{\mathrm{4}} +\mathrm{1}\right)\:\sqrt[{\mathrm{4}}]{{x}^{\mathrm{4}} +\mathrm{2}}}\:? \\ $$ Commented by liberty last updated on 20/Feb/21 $$\mathrm{I}\:=\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{4}} +\mathrm{1}\right)\:\sqrt[{\mathrm{4}}]{\mathrm{x}^{\mathrm{4}} +\mathrm{2}}} \\…

Solve-x-2-1-lt-5-

Question Number 67574 by pete last updated on 28/Aug/19 $$\mathrm{Solve}\:\mathrm{x}^{\mathrm{2}} +\mathrm{1}<−\mathrm{5} \\ $$ Commented by mathmax by abdo last updated on 28/Aug/19 $$\left({e}\right)\Rightarrow{x}^{\mathrm{2}} +\mathrm{6}<\mathrm{0}\:\:\:{impossible}\:{equation}\:\Rightarrow{no}\:{solution}\: \\…

f-0-1-R-f-0-1-f-2-dx-and-if-x-0-1-f-m-M-for-some-m-M-R-2-f-max-f-f-f-f-min-f-f-0-1-f-f-dx-then-f-e-x-f-f-f-x-f-f-f-f-0-f-f-0-f-0-do

Question Number 2032 by 123456 last updated on 31/Oct/15 $${f}:\left[\mathrm{0},+\mathrm{1}\right]\rightarrow\mathbb{R} \\ $$$$\eta\left({f}\right):=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}^{\mathrm{2}} {dx} \\ $$$$\mathrm{and}\:\mathrm{if}\:\forall{x}\in\left[\mathrm{0},\mathrm{1}\right],{f}\in\left[{m},\mathrm{M}\right]\:\mathrm{for}\:\mathrm{some}\:\left({m},\mathrm{M}\right)\in\mathbb{R}^{\mathrm{2}} \\ $$$${f}\uparrow:=\mathrm{max}\left({f}\right)−{f} \\ $$$${f}\downarrow:={f}−\mathrm{min}\left({f}\right) \\ $$$$\mu\left({f}\right):=\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}{f}\downarrow{f}\uparrow{dx}…