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as-we-can-know-for-Q-1-set-the-funvction-in-question-as-f-x-and-make-the-first-step-as-a-1-f-x-x-2-7x-3ln-x-df-x-2x-7-3-x-h-x-set-h-x-0-x-1-2-amp-x-3-so-the-monotonicity-of-f-x-is-f-n-l

Question Number 182657 by Strengthenchen last updated on 12/Dec/22 $${as}\:{we}\:{can}\:{know}\:{for}\:{Q}_{\mathrm{1}} ,\:{set}\:{the}\:{funvction}\:{in}\:{question}\:{as}\:{f}\left({x}\right) \\ $$$${and}\:{make}\:{the}\:{first}\:{step}\:{as}: \\ $$$${a}=\mathrm{1},{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{7}{x}+\mathrm{3ln}\:{x} \\ $$$${df}\left({x}\right)=\mathrm{2}{x}−\mathrm{7}+\frac{\mathrm{3}}{{x}}={h}\left({x}\right) \\ $$$${set}\:{h}\left({x}\right)=\mathrm{0}\Rightarrow{x}=\frac{\mathrm{1}}{\mathrm{2}}\&{x}=\mathrm{3} \\ $$$${so},{the}\:{monotonicity}\:{of}\:{f}\left({x}\right)\:{is}\:{f}\left({n}\right)<{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)_{\mid{n}<\frac{\mathrm{1}}{\mathrm{2}}} ,{f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)>{f}\left(\mathrm{2}\right),{f}\left(\mathrm{2}\right)<{f}\left({p}\underset{\mid{p}>\mathrm{2}.} {\right)} \\…

Question-117107

Question Number 117107 by Khalmohmmad last updated on 09/Oct/20 Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\mathrm{4}^{{x}} +\mathrm{6}^{{x}} =\mathrm{9}^{{x}} \\ $$$$\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{\mathrm{2}{x}} +\left(\frac{\mathrm{2}}{\mathrm{3}}\right)^{{x}} −\mathrm{1}=\mathrm{0} \\…

Question-117085

Question Number 117085 by mohammad17 last updated on 09/Oct/20 Answered by Dwaipayan Shikari last updated on 09/Oct/20 $$\int_{−\infty} ^{\infty} \frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$$$=\left[{tan}^{−\mathrm{1}} {x}\right]_{−\infty} ^{\infty}…

Question-182613

Question Number 182613 by sciencestudent last updated on 11/Dec/22 Answered by Acem last updated on 12/Dec/22 $$\:{Dis}.\:=\:{v}_{\mathrm{1}} \:\left({t}+\mathrm{4}\right)=\:{v}_{\mathrm{2}} \:\left({t}−\mathrm{2}\right) \\ $$$$\:\Rightarrow\:\frac{\mathrm{1}}{\mathrm{3}}\:\left({t}+\mathrm{4}\right)=\:\frac{\mathrm{5}}{\mathrm{12}}\:\left({t}−\mathrm{2}\right)\:,\:{t}=\:\mathrm{26}\:{min}\:_{\:\:\:\:\:\:\:\:\:\:\frac{\mathrm{5}}{\mathrm{12}}\:\:{the}\:{same}} ^{{Exp}\:\frac{\mathrm{1}}{\mathrm{3}}=\:\frac{{v}_{\mathrm{1}} }{\mathrm{60}}\:{conv}.\:{to}\:{min}} \\ $$$$\:{Dis}=\:{v}_{\mathrm{1}}…

How-many-5-digits-positive-integers-x-1-x-2-x-3-x-4-x-5-are-there-such-that-x-1-x-2-x-3-x-4-x-5-

Question Number 117061 by ZiYangLee last updated on 09/Oct/20 $$\mathrm{How}\:\mathrm{many}\:\mathrm{5}-\mathrm{digits}\:\mathrm{positive}\:\mathrm{integers} \\ $$$${x}_{\mathrm{1}} {x}_{\mathrm{2}} {x}_{\mathrm{3}} {x}_{\mathrm{4}} {x}_{\mathrm{5}} \:\mathrm{are}\:\mathrm{there}\:\mathrm{such}\:\mathrm{that}\: \\ $$$${x}_{\mathrm{1}} \leqslant{x}_{\mathrm{2}} \leqslant{x}_{\mathrm{3}} \leqslant{x}_{\mathrm{4}} \leqslant{x}_{\mathrm{5}} ? \\…

Transform-into-factorial-form-the-following-A-1-3-5-7-9-2n-1-Example-4-3-2-1-4-

Question Number 182584 by Matica last updated on 11/Dec/22 $$\:\:{Transform}\:{into}\:{factorial}\:{form}\:{the}\:{following} \\ $$$$\:\:{A}\:=\:\mathrm{1}×\mathrm{3}×\mathrm{5}×\mathrm{7}×\mathrm{9}×…×\left(\mathrm{2}{n}−\mathrm{1}\right)\:.\: \\ $$$${Example}:\:\mathrm{4}×\mathrm{3}×\mathrm{2}×\mathrm{1}=\mathrm{4}! \\ $$ Answered by aleks041103 last updated on 11/Dec/22 $${A}=\mathrm{1}.\mathrm{3}.\mathrm{5}.\mathrm{7}…\left(\mathrm{2}{n}−\mathrm{1}\right)=\frac{\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}.\mathrm{6}.\mathrm{7}…\left(\mathrm{2}{n}−\mathrm{1}\right).\mathrm{2}{n}}{\mathrm{2}.\mathrm{4}.\mathrm{6}….\left(\mathrm{2}{n}\right)}= \\…

f-x-x-2-4x-3-x-2-3-f-1-x-

Question Number 182581 by sciencestudent last updated on 11/Dec/22 $${f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{3}}{{x}^{\mathrm{2}} −\mathrm{3}}\:\:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=? \\ $$ Answered by cortano1 last updated on 11/Dec/22 $$\:\mathrm{yx}^{\mathrm{2}}…