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Category: Differentiation

Question-29778

Question Number 29778 by puneet1789 last updated on 12/Feb/18 Answered by Giannibo last updated on 12/Feb/18 $$ \\ $$$$ \\ $$$$\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{1} \\ $$$$\mathrm{e}^{\mathrm{x}} \mathrm{f}\left(\mathrm{x}\right)+\mathrm{e}^{\mathrm{x}} \mathrm{f}'\left(\mathrm{x}\right)\leqslant\mathrm{e}^{\mathrm{x}}…

Question-160837

Question Number 160837 by mnjuly1970 last updated on 07/Dec/21 Commented by cortano last updated on 07/Dec/21 $$\Leftrightarrow\:\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} −\mathrm{2x}^{\mathrm{2}} +\mathrm{1}=\mathrm{x}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{1}\right) \\ $$$$\Leftrightarrow\mathrm{x}^{\mathrm{4}} −\mathrm{x}^{\mathrm{2}} +\mathrm{1}\:=\:\mathrm{x}^{\mathrm{3}}…

x-x-2-1-y-y-2-1-2021-x-y-R-min-x-y-

Question Number 160603 by cortano last updated on 03/Dec/21 $$\:\left(\mathrm{x}+\sqrt{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\left(\mathrm{y}+\sqrt{\mathrm{y}^{\mathrm{2}} +\mathrm{1}}\right)=\mathrm{2021} \\ $$$$\:\forall\mathrm{x},\mathrm{y}\in\mathbb{R}^{+} \:.\:\mathrm{min}\:\left(\mathrm{x}+\mathrm{y}\right)=? \\ $$ Answered by MJS_new last updated on 03/Dec/21 $$\mathrm{of}\:\mathrm{all}\:\mathrm{rectangles}\:\mathrm{with}\:\mathrm{sides}\:{a},\:{b}\:\mathrm{and}\:\mathrm{given}…

0-1-tan-1-x-ln-x-solution-f-a-0-1-tan-1-x-x-a-dx-n-1-1-n-1-2n-1-0-1-x-2n-a-1-dx-

Question Number 160577 by mnjuly1970 last updated on 02/Dec/21 $$ \\ $$$$\:\:\:\:\:\Omega=\int_{\mathrm{0}} ^{\:\mathrm{1}} {tan}^{\:−\mathrm{1}} \:\left({x}\right).{ln}\left({x}\right)\:=\:? \\ $$$$\:\:\:\:\:−−−−{solution}−−−− \\ $$$$\:\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\:\mathrm{1}} {tan}^{\:−\mathrm{1}} \left(\:{x}\right)\:.{x}^{\:{a}} {dx} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\underset{{n}=\mathrm{1}}…

A-gas-expands-according-to-the-law-PV-K-constant-Initialy-v-1000cubic-metres-and-p-40N-m-2-If-the-pressure-is-decreased-at-the-rate-of-5N-m-2-min-find-the-rate-at-which-the-gas-is-expanding-wh

Question Number 29490 by Victor31926 last updated on 09/Feb/18 $$\mathrm{A}\:\mathrm{gas}\:\mathrm{expands}\:\mathrm{according}\:\mathrm{to}\:\mathrm{the}\:\mathrm{law}\:\mathrm{PV}=\mathrm{K}\:\left(\mathrm{constant}\right). \\ $$$$\mathrm{Initialy},\:\boldsymbol{\mathrm{v}}=\mathrm{1000cubic}\:\mathrm{metres}\:\mathrm{and}\:\boldsymbol{\mathrm{p}}=\mathrm{40N}/\mathrm{m}^{\mathrm{2}} . \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{pressure}\:\mathrm{is}\:\mathrm{decreased}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{5N}/\mathrm{m}^{\mathrm{2}} /\mathrm{min}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{at}\:\mathrm{which} \\ $$$$\mathrm{the}\:\mathrm{gas}\:\mathrm{is}\:\mathrm{expanding}\:\mathrm{when}\:\mathrm{its}\:\mathrm{volume}\:\mathrm{is}\:\mathrm{2000cubic}\:\mathrm{metres}. \\ $$$$ \\ $$ Answered by Rasheed.Sindhi…