Category: Differentiation

Question Number 35248 by Raj Singh last updated on 17/May/18 Commented by Joel579 last updated on 17/May/18 $$\mathrm{Would}\mathrm{u}\mathrm{like}\mathrm{to}\mathrm{translate}\mathrm{into}\mathrm{English}?$$ Terms of Service Privacy Policy…

Question Number 166257 by mnjuly1970 last updated on 16/Feb/22 $$$$$$\lfloor x\rfloor \lfloor 2x\rfloor \lfloor 3x\rfloor =6$$$$x=\stackrel{}{?}$$ Commented by MJS_new last updated on 16/Feb/22 $$\mathrm{1}\leqslant{x}<\frac{\mathrm{4}}{\mathrm{3}}…

Question Number 166246 by mnjuly1970 last updated on 16/Feb/22 Answered by Mathspace last updated on 18/Feb/22 $$I{=}_{byparts}{\left[(1-\frac{1}{x}){ln}^2(1-x^2)\right]}_0^1$$$$−\int_{\mathrm{0}} ^{\mathrm{1}} \left(\mathrm{1}−\frac{\mathrm{1}}{{x}}\right).\mathrm{2}{ln}\left(\mathrm{1}−{x}^{\mathrm{2}}…

Question Number 166082 by mnjuly1970 last updated on 12/Feb/22 $$$$$$prove$$$$\mathrm{\Omega }={\int }_0^1\frac{{(1-x)}^2.{ln}^3(1-x)}{x}dx=\frac{51}{8}-\frac{{\pi }^4}{15}\mathrm{<img\; draggable="false"\; role="img"\; class="emoji"\; alt="◼"\; src="https://s.w.org/images/core/emoji/15.1.0/svg/25fc.svg">}m.n$$$$$$$$$$…

Question Number 100388 by Ar Brandon last updated on 26/Jun/20 $$\mathcal{G}\mathrm{iven}\mathrm{f}:[0,2]\to \mathbb{R},\mathrm{f}\left(\mathrm{x}\right)\mathrm{is}\mathrm{twice}\mathrm{derivable}\mathrm{and}$$$$\mathrm{f}\left(0\right)=\mathrm{f}\left(1\right)=\mathrm{f}\left(2\right)=0$$$$i-\mathcal{S}\mathrm{how}\mathrm{that}\mathrm{there}\mathrm{exist}{\mathrm{c}}_1,{\mathrm{c}}_2,\mathrm{such}\mathrm{that}{\mathrm{f}}^{\prime }\left({\mathrm{c}}_1\right)=0$$$$\mathrm{and}{\mathrm{f}}^{\prime }\left({\mathrm{c}}_2\right)=0$$$${ii}-\mathcal{S}\mathrm{how}\:\mathrm{that}\:\mathrm{there}\:\mathrm{exist}\:\mathrm{c}_{\mathrm{3}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{f}''\left(\mathrm{c}_{\mathrm{3}} \right)=\mathrm{0}…