Menu Close

Author: Tinku Tara

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

Question Number 132070 by bramlexs22 last updated on 10/Feb/21 $$\mathrm{I}=\int\:\frac{\mathrm{x}}{\left(\mathrm{x}^{\mathrm{4}} −\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx}\:? \\ $$ Answered by liberty last updated on 10/Feb/21 $$\mathrm{I}=\:\frac{\mathrm{1}}{\mathrm{2}}\int\:\frac{\mathrm{d}\left(\mathrm{x}^{\mathrm{2}} \right)}{\left(\left(\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{2}}…

3-3x-4-3-x-2-4-

Question Number 991 by Madan pd gupta last updated on 13/May/15 $$\mathrm{3}\left(\mathrm{3}{x}−\mathrm{4}\right)+\mathrm{3}\left({x}−\mathrm{2}\right)=\mathrm{4} \\ $$ Answered by prakash jain last updated on 13/May/15 $$\mathrm{9}{x}−\mathrm{12}+\mathrm{3}{x}−\mathrm{6}=\mathrm{0} \\ $$$$\mathrm{12}{x}=\mathrm{18}\Rightarrow{x}=\frac{\mathrm{18}}{\mathrm{12}}=\frac{\mathrm{3}}{\mathrm{2}}…

Question-66527

Question Number 66527 by mr W last updated on 16/Aug/19 Commented by mr W last updated on 16/Aug/19 $${the}\:{perimeter}\:{of}\:{a}\:{rope}\:{loop}\:{is}\:{L}. \\ $$$${now}\:{it}\:{is}\:{hanged}\:{on}\:{two}\:{pins}\:{A}\:{and}\:{B}. \\ $$$${the}\:{distance}\:{between}\:{the}\:{pins}\:{is}\:{b}.\: \\ $$$${all}\:{contact}\:{is}\:{frictionless}.…

Show-that-x-x-1-3x-1-gt-1-given-that-x-gt-1-3-

Question Number 984 by 112358 last updated on 13/May/15 $${Show}\:{that}\:\frac{{x}\left({x}+\mathrm{1}\right)}{\mathrm{3}{x}−\mathrm{1}}>\mathrm{1}\:{given}\:{that}\:{x}>\frac{\mathrm{1}}{\mathrm{3}}\:. \\ $$ Commented by prakash jain last updated on 13/May/15 $$\mathrm{For}\:{x}=\mathrm{1}\:\mathrm{LHS}=\frac{\mathrm{1}×\mathrm{2}}{\mathrm{2}}=\mathrm{1}\ngtr\mathrm{1} \\ $$$$\mathrm{So}\:\mathrm{the}\:\mathrm{inequality}\:\mathrm{should}\:\mathrm{be} \\ $$$$\frac{{x}\left({x}+\mathrm{1}\right)}{\mathrm{3}{x}−\mathrm{1}}\geqslant\mathrm{1}…

Question-66518

Question Number 66518 by Masumsiddiqui399@gmail.com last updated on 16/Aug/19 Commented by mathmax by abdo last updated on 16/Aug/19 $${let}\:{f}\left({x}\right)=\frac{{x}\sqrt{{x}}−{a}\sqrt{{a}}}{{x}−{a}}\:\:\:{cha}\mathrm{7}{gement}\:{x}−{a}={t}\:{give} \\ $$$${lim}_{{x}\rightarrow{a}} {f}\left({x}\right)\:={lim}_{{t}\rightarrow\mathrm{0}} \:\:\:\frac{\left({t}+{a}\right)\sqrt{{t}+{a}}−{a}\sqrt{{a}}}{{t}} \\ $$$$={lim}_{{t}\rightarrow\mathrm{0}}…