Menu Close

Author: Tinku Tara

Question-206637

Question Number 206637 by jshfnahdj last updated on 21/Apr/24 Answered by Frix last updated on 21/Apr/24 $${x}^{{y}} \:\mathrm{with}\:{x},\:{y}\:\in\mathbb{C} \\ $$$$\mathrm{We}\:\mathrm{need}\:{x}={r}\mathrm{e}^{\mathrm{i}\theta} \:\mathrm{and}\:{y}={a}+{b}\mathrm{i}\:\Rightarrow \\ $$$${x}^{{y}} =\left({r}\mathrm{e}^{\mathrm{i}\theta} \right)^{{a}+{b}\mathrm{i}}…

Question-206639

Question Number 206639 by mathlove last updated on 21/Apr/24 Commented by Frix last updated on 21/Apr/24 $$=\underset{\frac{\pi}{\mathrm{12}}} {\overset{\frac{\pi}{\mathrm{11}}} {\int}}\left(\frac{\sqrt{{s}}}{\mathrm{2}\left(\sqrt{{c}}+\sqrt{{s}}\right)}−\frac{\sqrt{{cs}}}{{c}+\sqrt{{s}}\left(\sqrt{{c}}+\mathrm{1}\right)}+\frac{\left(\sqrt{{c}}−\mathrm{1}\right){s}+\sqrt{{cs}}}{\mathrm{2}\left(\left(\sqrt{{s}}+\mathrm{1}\right){c}+\left(\sqrt{{c}}+\mathrm{1}\right){s}\right)}\right){dx} \\ $$$$\mathrm{With}\:{c}=\mathrm{cos}\:{x}\:\wedge{s}=\mathrm{sin}\:{x} \\ $$$$\mathrm{I}\:\mathrm{doubt}\:\mathrm{we}\:\mathrm{can}\:\mathrm{solve}\:\mathrm{this}. \\ $$…

Question-206616

Question Number 206616 by universe last updated on 20/Apr/24 Answered by aleks041103 last updated on 21/Apr/24 $${e}^{\mathrm{3}{x}} \:{is}\:{increasing}\:{and}\:{continuous}\:{for}\:{x}>\mathrm{0} \\ $$$${ln}\left({x}\right)\:{is}\:{incr}.\:{and}\:{cont}.\:{for}\:{x}>\mathrm{0} \\ $$$$\Rightarrow{f}\left({x}\right)\:{is}\:{incr}.\:{and}\:{cont}.\:{for}\:{x}>\mathrm{0} \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\:{f}\left({x}\right)\rightarrow−\infty…

If-A-sin-4-cos-4-then-select-the-correct-option-i-0-lt-A-lt-1-2-ii-1-lt-A-lt-3-2-iii-1-2-A-1-iv-3-2-A-2-

Question Number 206618 by MATHEMATICSAM last updated on 20/Apr/24 $$\mathrm{If}\:\mathrm{A}\:=\:\mathrm{sin}^{\mathrm{4}} \theta\:+\:\mathrm{cos}^{\mathrm{4}} \theta\:\mathrm{then}\:\mathrm{select}\:\mathrm{the}\: \\ $$$$\mathrm{correct}\:\mathrm{option}: \\ $$$$\left.\mathrm{i}\right)\:\mathrm{0}\:<\:\mathrm{A}\:<\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.\mathrm{ii}\right)\:\mathrm{1}\:<\:\mathrm{A}\:<\:\frac{\mathrm{3}}{\mathrm{2}} \\ $$$$\left.\mathrm{iii}\right)\:\frac{\mathrm{1}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{1} \\ $$$$\left.\mathrm{iv}\right)\:\frac{\mathrm{3}}{\mathrm{2}}\:\leq\:\mathrm{A}\:\leq\:\mathrm{2} \\ $$ Answered…

If-f-x-x-2-x-2-f-x-3-x-gt-2-Find-1-53-f-x-dx-

Question Number 206613 by hardmath last updated on 20/Apr/24 $$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\begin{cases}{\mathrm{x}^{\mathrm{2}} \:\:\:,\:\:\:\mathrm{x}\:\leqslant\:\mathrm{2}}\\{\mathrm{f}\left(\mathrm{x}−\mathrm{3}\right)\:\:\:,\:\:\:\mathrm{x}\:>\:\mathrm{2}}\end{cases} \\ $$$$\mathrm{Find}\:\:\:\int_{−\mathrm{1}} ^{\:\mathrm{53}} \:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by MM42 last updated on 20/Apr/24 $$\mathrm{57}…