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Author: Tinku Tara

Find-a-b-c-which-fulfill-lim-x-0-x-a-b-cos-x-c-sin-x-x-5-1-

Question Number 66544 by naka3546 last updated on 17/Aug/19 $${Find}\:\:{a},\:{b},\:{c}\:\:{which}\:\:{fulfill}\:\:\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\:\frac{{x}\left({a}\:+\:{b}\:\mathrm{cos}\:{x}\right)\:−\:{c}\:\mathrm{sin}\:{x}}{{x}^{\mathrm{5}} }\:\:=\:\:\mathrm{1} \\ $$ Answered by Tanmay chaudhury last updated on 17/Aug/19 $$\underset{{x}\rightarrow\mathrm{0}}…

Solve-dx-1-x-2-3-

Question Number 132082 by liberty last updated on 11/Feb/21 $$\:\mathrm{Solve}\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{1}+\mathrm{x}^{\mathrm{2}} \right)^{\mathrm{3}} }\:?\: \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\mathrm{Ostrogradski}\:\mathrm{method} \\ $$$$\mathrm{Consider}\:\frac{\mathrm{d}}{\mathrm{dx}}\left(\frac{\mathrm{ax}^{\mathrm{3}} +\mathrm{bx}}{\left(\mathrm{x}^{\mathrm{2}}…

x-2-gt-2-x-

Question Number 1007 by tera last updated on 13/May/15 $$\left[{x}−\mathrm{2}\right]>−\mathrm{2}\:.\:\:{x}=….. \\ $$ Answered by prakash jain last updated on 13/May/15 $$\left({x}−\mathrm{2}\right)>−\mathrm{2}\Rightarrow{x}−\mathrm{2}+\mathrm{2}>−\mathrm{2}+\mathrm{2}\Rightarrow{x}>\mathrm{0} \\ $$ Terms of…

Given-the-function-f-x-0-x-1-t-3-1-2-dt-If-h-x-is-the-inverse-of-f-x-and-h-x-is-derivative-of-h-x-Find-the-value-of-h-x-h-x-2-

Question Number 132076 by liberty last updated on 11/Feb/21 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left({x}\right)=\int_{\mathrm{0}} ^{\:{x}} \left(\mathrm{1}+{t}^{\mathrm{3}} \right)^{−\mathrm{1}/\mathrm{2}} {dt}. \\ $$$$\mathrm{If}\:\mathrm{h}\left({x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{inverse}\:\mathrm{of}\:\mathrm{f}\left({x}\right)\:\mathrm{and}\:\mathrm{h}'\left({x}\right) \\ $$$$\mathrm{is}\:\mathrm{derivative}\:\mathrm{of}\:\mathrm{h}\left({x}\right).\:\mathrm{Find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{h}''\left({x}\right)}{\left(\mathrm{h}\left(\mathrm{x}\right)\right)^{\mathrm{2}} }\:. \\ $$$$ \\ $$…

3-x-3x-x-

Question Number 66543 by hmamarques1994@gmail.com last updated on 17/Aug/19 $$\:\mathrm{3}^{\boldsymbol{{x}}} =\mathrm{3}\boldsymbol{{x}} \\ $$$$\: \\ $$$$\:\boldsymbol{{x}}=? \\ $$ Commented by gunawan last updated on 17/Aug/19 $${x}=\mathrm{1}…

If-L-lim-x-pi-4-tan-3-x-tan-x-cos-x-pi-4-then-L-4-

Question Number 132079 by liberty last updated on 11/Feb/21 $$\mathrm{If}\:\mathrm{L}\:=\:\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{tan}\:^{\mathrm{3}} \mathrm{x}−\mathrm{tan}\:\mathrm{x}}{\mathrm{cos}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)} \\ $$$$\mathrm{then}\:\frac{\mathrm{L}}{\mathrm{4}}\:=? \\ $$ Answered by EDWIN88 last updated on 11/Feb/21 $$\:\mathrm{L}=\underset{{x}\rightarrow\pi/\mathrm{4}} {\mathrm{lim}}\frac{\mathrm{tan}\:\mathrm{x}\left(\mathrm{tan}\:\mathrm{x}+\mathrm{1}\right)\left(\mathrm{tan}\:\mathrm{x}−\mathrm{1}\right)}{\mathrm{cos}\:\left(\mathrm{x}+\frac{\pi}{\mathrm{4}}\right)}…