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Author: Tinku Tara

1-e-e-ln-x-dx-

Question Number 88902 by M±th+et£s last updated on 13/Apr/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} {ln}\mid{x}\mid\:{dx} \\ $$ Commented by abdomathmax last updated on 13/Apr/20 $$\int_{\frac{\mathrm{1}}{{e}}} ^{{e}} \:{ln}\mid{x}\mid{dx}\:=\left[{xlnx}−{x}\right]_{\frac{\mathrm{1}}{{e}}} ^{{e}}…

find-lim-x-0-ln-sin-3x-cos-3x-ln-sin-x-cos-x-

Question Number 88896 by M±th+et£s last updated on 13/Apr/20 $${find}\: \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {{lim}}\frac{{ln}\left({sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\right)}{{ln}\left({sin}\left({x}\right)+{cos}\left({x}\right)\right)} \\ $$ Commented by abdomathmax last updated on 13/Apr/20 $${let}\:{f}\left({x}\right)=\frac{{ln}\left({sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\right)}{{ln}\left({sinx}+{cosx}\right)}\:\:{we}\:{have} \\ $$$${sin}\left(\mathrm{3}{x}\right)+{cos}\left(\mathrm{3}{x}\right)\sim\mathrm{3}{x}\:+\mathrm{1}−\frac{\left(\mathrm{3}{x}\right)^{\mathrm{2}}…

A-50-g-lead-bullet-sp-heat-0-02-is-initially-at-30-C-It-is-fired-vertically-upwards-with-a-speed-of-840-m-s-and-on-returning-to-the-starting-level-strikes-a-cake-of-ice-at-0-C-How-much-ice-is-melt

Question Number 23361 by Tinkutara last updated on 29/Oct/17 $$\mathrm{A}\:\mathrm{50}\:\mathrm{g}\:\mathrm{lead}\:\mathrm{bullet},\:\mathrm{sp}.\:\mathrm{heat}\:\mathrm{0}.\mathrm{02}\:\mathrm{is} \\ $$$$\mathrm{initially}\:\mathrm{at}\:\mathrm{30}°\mathrm{C}.\:\mathrm{It}\:\mathrm{is}\:\mathrm{fired}\:\mathrm{vertically} \\ $$$$\mathrm{upwards}\:\mathrm{with}\:\mathrm{a}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{840}\:\mathrm{m}/\mathrm{s}\:\mathrm{and} \\ $$$$\mathrm{on}\:\mathrm{returning}\:\mathrm{to}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{level}\:\mathrm{strikes} \\ $$$$\mathrm{a}\:\mathrm{cake}\:\mathrm{of}\:\mathrm{ice}\:\mathrm{at}\:\mathrm{0}°\mathrm{C}.\:\mathrm{How}\:\mathrm{much}\:\mathrm{ice}\:\mathrm{is} \\ $$$$\mathrm{melted}?\:\mathrm{Assume}\:\mathrm{that}\:\mathrm{all}\:\mathrm{energy}\:\mathrm{is} \\ $$$$\mathrm{spent}\:\mathrm{in}\:\mathrm{melting}\:\mathrm{only}\:\left({L}\:=\:\mathrm{80}\:\mathrm{cal}/\mathrm{g}\right). \\ $$ Answered…

Question-154429

Question Number 154429 by liberty last updated on 18/Sep/21 Commented by liberty last updated on 18/Sep/21 $$ \\ $$$$\:{A}=\sqrt[{\mathrm{3}}]{−\mathrm{15}+\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}}+\sqrt[{\mathrm{3}}]{−\mathrm{15}−\frac{\mathrm{28}\sqrt{\mathrm{3}}{i}}{\mathrm{9}}} \\ $$$$ \\ $$ Commented by…