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Author: Tinku Tara

calculus-preliminary-Q-f-x-2-x-2-x-f-1-x-solution-y-2-x-2-x-y-2-2x-1-2-x-2-2x-y2-x-1-0-2-x-t-

Question Number 135215 by mnjuly1970 last updated on 11/Mar/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:…..{calculus}\:{preliminary}…. \\ $$$$\:\:\:{Q}:\:{f}\left({x}\right)=\mathrm{2}^{{x}} −\mathrm{2}^{−{x}} \:\Rightarrow\:{f}^{\:−\mathrm{1}} \left({x}\right)=??? \\ $$$$\:\:{solution}: \\ $$$$\:\:\:\:\:{y}=\mathrm{2}^{{x}} −\mathrm{2}^{−{x}} \:\:\:….. \\ $$$$\:\:\:\:\:\:{y}=\frac{\mathrm{2}^{\mathrm{2}{x}} −\mathrm{1}}{\mathrm{2}^{{x}} }\:\Rightarrow\mathrm{2}^{\mathrm{2}{x}}…

Four-persons-a-b-c-d-are-standing-at-four-vertices-of-square-ABCD-All-four-start-moving-simultaneously-such-a-is-always-moving-towards-b-on-a-straight-line-between-a-and-b-Similary-b-is-always-mo

Question Number 4140 by prakash jain last updated on 29/Dec/15 $$\mathrm{Four}\:\mathrm{persons}\:\mathrm{a},\:\mathrm{b},\:\mathrm{c},\:\mathrm{d}\:\mathrm{are}\:\mathrm{standing}\:\mathrm{at}\:\mathrm{four} \\ $$$$\mathrm{vertices}\:\mathrm{of}\:\mathrm{square}\:\mathrm{ABCD}. \\ $$$$\mathrm{All}\:\mathrm{four}\:\mathrm{start}\:\mathrm{moving}\:\mathrm{simultaneously}\:\mathrm{such} \\ $$$$\boldsymbol{\mathrm{a}}\:\mathrm{is}\:\mathrm{always}\:\mathrm{moving}\:\mathrm{towards}\:\boldsymbol{\mathrm{b}}\:\mathrm{on}\:\mathrm{a}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{between}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\boldsymbol{\mathrm{b}}.\:\mathrm{Similary}\:\boldsymbol{\mathrm{b}}\:\mathrm{is}\:\mathrm{always} \\ $$$$\mathrm{moving}\:\mathrm{directly}\:\mathrm{towards}\:\boldsymbol{\mathrm{c}},\:\boldsymbol{\mathrm{c}}\:\mathrm{is}\:\mathrm{directly} \\ $$$$\mathrm{moving}\:\mathrm{towards}\:\boldsymbol{\mathrm{d}}\:\mathrm{and}\:\boldsymbol{\mathrm{d}}\:\mathrm{is}\:\mathrm{directly}\:\mathrm{moving} \\ $$$$\mathrm{towards}\:\boldsymbol{\mathrm{a}}.…

Find-minimum-value-of-function-f-x-4x-2-8x-13-6-1-x-

Question Number 135211 by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{function} \\ $$$$\mathrm{f}\left(\mathrm{x}\right)\:=\:\frac{\mathrm{4x}^{\mathrm{2}} +\mathrm{8x}+\mathrm{13}}{\mathrm{6}\left(\mathrm{1}+\mathrm{x}\right)} \\ $$ Commented by mr W last updated on 11/Mar/21 $$\underset{{x}\rightarrow−\mathrm{1}^{−} }…

Question-135204

Question Number 135204 by victoras last updated on 11/Mar/21 Answered by benjo_mathlover last updated on 11/Mar/21 $$\mathrm{81}^{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \:+\:\mathrm{81}^{\mathrm{1}−\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \:=\:\mathrm{30} \\ $$$$\mathrm{let}\:\mathrm{81}^{\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}} \:=\:\mathrm{z}\:…

What-are-the-neccesary-and-sufficient-conditions-so-that-n-0-f-n-x-dx-n-0-f-n-x-dx-

Question Number 4133 by prakash jain last updated on 29/Dec/15 $$\mathrm{What}\:\mathrm{are}\:\mathrm{the}\:\mathrm{neccesary}\:\mathrm{and}\:\mathrm{sufficient} \\ $$$$\mathrm{conditions}\:\mathrm{so}\:\mathrm{that} \\ $$$$\int_{−\infty} ^{\:+\infty} \left[\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}{f}\left({n},{x}\right)\right]{dx}=\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\int_{−\infty} ^{+\infty} {f}\left({n},{x}\right){dx}\right] \\ $$…

Question-135206

Question Number 135206 by victoras last updated on 11/Mar/21 Answered by Olaf last updated on 11/Mar/21 $$\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} {x}} +\mathrm{81}^{\mathrm{cos}^{\mathrm{2}} {x}} \:=\:\mathrm{30} \\ $$$$\mathrm{81}^{\mathrm{sin}^{\mathrm{2}} {x}} +\frac{\mathrm{81}}{\mathrm{81}^{\mathrm{sin}^{\mathrm{2}}…