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Category: Differentiation

Question-188534

Question Number 188534 by thotasandeep111 last updated on 03/Mar/23 Answered by mr W last updated on 03/Mar/23 $$\int{f}\left({x}\right){dx}={f}\left({x}\right) \\ $$$$\Rightarrow{f}\left({x}\right)={e}^{{x}} \\ $$$$\int\left({f}\left({x}\right)\right)^{\mathrm{2}} {dx}=\int{e}^{\mathrm{2}{x}} {dx}=\frac{{e}^{\mathrm{2}{x}} }{\mathrm{2}}+{C}=\frac{\left({f}\left({x}\right)\right)^{\mathrm{2}}…

solve-x-1-y-1-x-y-x-e-2x-

Question Number 57415 by Abdo msup. last updated on 03/Apr/19 $${solve}\:\left({x}−\mathrm{1}\right){y}^{'} \:+\left(\mathrm{1}+\sqrt{{x}}\right){y}\:={x}\:{e}^{−\mathrm{2}{x}} \\ $$ Commented by maxmathsup by imad last updated on 12/Apr/19 $${due}\:{to}\:\sqrt{{x}}{we}\:{must}\:{have}\:{x}\geqslant\mathrm{0}\:\:\:\left({ed}\right)\:\Leftrightarrow\left(\sqrt{{x}}−\mathrm{1}\right)\left(\sqrt{{x}}+\mathrm{1}\right){y}^{'} +\left(\sqrt{\:{x}}+\mathrm{1}\right){y}\:={xe}^{−\mathrm{2}{x}}…

Question-188387

Question Number 188387 by cortano12 last updated on 28/Feb/23 Answered by Frix last updated on 28/Feb/23 $$\mathrm{I}\:\mathrm{think}\:\mathrm{because}\:\mathrm{of}\:\mathrm{symmetry}\:{a}={b}={c}=\mathrm{1}\:\Rightarrow \\ $$$$\mathrm{Minimum}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$ Answered by mnjuly1970 last…

general-calculus-i-1-1-4x-n-0-2n-n-x-n-ii-pi-2-n-0-2n-n-4-n-1-2n-1-

Question Number 122704 by mnjuly1970 last updated on 19/Nov/20 $$\:\:\:\:\:\:\:\:\:\:\:…\:{general}\:\:{calculus}… \\ $$$$\:{i}:\:\:\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{1}−\mathrm{4}{x}}}\:\overset{??} {=}\underset{{n}=\mathrm{0}\:} {\overset{\infty} {\sum}}\left[\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}\:\:{x}^{{n}} \right] \\ $$$$\:{ii}:\:\frac{\pi}{\mathrm{2}}\:\overset{?} {=}\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\frac{\begin{pmatrix}{\mathrm{2}{n}}\\{\:{n}}\end{pmatrix}}{\mathrm{4}^{{n}} }\:\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)}\right] \\ $$$$\:\:\:\:\:\:\:\:\:\: \\…

Question-57084

Question Number 57084 by frimpshaddie last updated on 30/Mar/19 Commented by Kunal12588 last updated on 30/Mar/19 $$\left({d}\right)\:{when}\:{the}\:{velocity}\:{of}\:{particle}\:{becomes}\:\mathrm{0} \\ $$$${then}\:{the}\:{particle}\:{is}\:{said}\:{to}\:{be}\:{in}\:{rest} \\ $$$$\left({horizontal}\:{motion}\:{only}\right) \\ $$$$\therefore{v}=\mathrm{0} \\ $$$$\Rightarrow\mathrm{3}{t}^{\mathrm{2}}…