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Author: Tinku Tara

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}}…

Is-there-f-n-such-that-lim-x-0-n-1-f-n-x-n-0-f-n-is-independent-of-x-

Question Number 4132 by prakash jain last updated on 29/Dec/15 $$\mathrm{Is}\:\mathrm{there}\:{f}\left({n}\right)\:\mathrm{such}\:\mathrm{that} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\left[\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:{f}\left({n}\right){x}^{{n}} \right]\neq\mathrm{0} \\ $$$${f}\left({n}\right)\:\mathrm{is}\:\mathrm{independent}\:\mathrm{of}\:{x}. \\ $$ Commented by Yozzii last…

Question-69667

Question Number 69667 by ahmadshahhimat775@gmail.com last updated on 26/Sep/19 Answered by Kunal12588 last updated on 26/Sep/19 $$\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {{lim}}\frac{{sec}\:{x}\:−\mathrm{2}}{\frac{\pi}{\mathrm{3}}−{x}} \\ $$$$=\underset{{x}\rightarrow\frac{\pi}{\mathrm{3}}} {{lim}}\frac{{sec}\:{x}\:{tan}\:{x}}{−\mathrm{1}} \\ $$$$=−\mathrm{2}×\sqrt{\mathrm{3}}=−\mathrm{2}\sqrt{\mathrm{3}} \\ $$…