Question Number 226880 by Spillover last updated on 17/Dec/25 Answered by TonyCWX last updated on 18/Dec/25 $$\int_{\mathrm{0}} ^{\mathrm{1}} \left[\mathrm{2}^{{x}} \right]\mathrm{d}{x} \\ $$$$=\:\int_{\mathrm{0}} ^{\mathrm{1}} \left[{e}^{{x}\mathrm{ln}\left(\mathrm{2}\right)} \right]\mathrm{d}{x}…
Question Number 226882 by hardmath last updated on 17/Dec/25 Answered by breniam last updated on 17/Dec/25 $$=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}}{\:\frac{\sqrt[{{n}}]{\mathrm{2}^{{n}+\mathrm{1}} }−\mathrm{1}}{\:\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}}}=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{{n}\left(\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}\right)}{\mathrm{2}\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}} \\ $$$$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\left(\mathrm{2}\sqrt[{{n}}]{\mathrm{2}}−\mathrm{1}\right)=\mathrm{2}−\mathrm{1}=\mathrm{1} \\ $$$$\underset{{x}\rightarrow\infty}…
Question Number 226812 by mr W last updated on 15/Dec/25 $${if}\:\mathrm{28}{x}+\mathrm{30}{y}+\mathrm{31}{z}=\mathrm{360}\:{with}\:{x},\:{y},\:{z} \\ $$$${being}\:{positive}\:{integers},\:{find} \\ $$$${x}+{y}+{z}=? \\ $$ Commented by Ghisom_ last updated on 15/Dec/25 $$\mathrm{12}…
Question Number 226766 by mr W last updated on 13/Dec/25 Answered by mahdipoor last updated on 13/Dec/25 $$\mathrm{if}\:\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{ax}+\mathrm{b}\:\Rightarrow \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{2x}+\mathrm{1}\:\mathrm{or}\:−\mathrm{2x}−\mathrm{3} \\ $$$$\mathrm{but}\:\mathrm{its}\:\mathrm{only}\:\mathrm{answer}? \\ $$$$\mathrm{all}\:\mathrm{function}\:\mathrm{can}\:\mathrm{show}\:\mathrm{as}\:\mathrm{f}\left(\mathrm{x}\right)=\underset{\mathrm{i}=\mathrm{0}} {\overset{\mathrm{m}}…
Question Number 226743 by MrAjder last updated on 12/Dec/25 $$ \\ $$$${Prove}:\frac{\mathrm{1}}{\mathrm{2}{ne}}<\frac{\mathrm{1}}{{e}}−\left(\mathrm{1}−\frac{\mathrm{1}}{{n}}\right)^{{n}} <\frac{\mathrm{1}}{{ne}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 226728 by hardmath last updated on 11/Dec/25 $$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\frac{\boldsymbol{\pi}}{\mathrm{4}}} \:\frac{\mathrm{dx}}{\mathrm{1}\:+\:\mathrm{sin}^{\mathrm{2}} \mathrm{x}}\:=\:? \\ $$ Answered by Ghisom_ last updated on 12/Dec/25 $$\mathrm{there}'\mathrm{s}\:\mathrm{an}\:\mathrm{easy}\:\mathrm{but}\:\mathrm{boring}\:\mathrm{solution}\:\mathrm{using} \\ $$$${t}=\mathrm{tan}\:{x}…
Question Number 226713 by ajfour last updated on 11/Dec/25 $$\:\:{If}\: \\ $$$${p}=\frac{\mathrm{1}}{{x}}−\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$${what}\:{should}\:{p}=\frac{\left({N}\right)_{\mathrm{4}} }{\left({D}\right)_{\mathrm{4}} } \\ $$$$\left({N}\right)_{\mathrm{4}} \:{means}\:{numerator}\:{of}\:{p}\:\:{in} \\ $$$${quaternary}\:{for}\:{x}\:{to}\:{be}\:\mathrm{777}? \\ $$ Terms…
Question Number 226687 by fantastic2 last updated on 10/Dec/25 $${im}\:{back}\:{guys}! \\ $$$${my}\:{exams}\:{are}\:{over} \\ $$$$ \\ $$ Commented by fantastic2 last updated on 10/Dec/25 $${efgh} \\…
Question Number 226675 by hardmath last updated on 10/Dec/25 Commented by hardmath last updated on 10/Dec/25 $$ \\ $$The image is not fully displayed, the…
Question Number 226603 by Spillover last updated on 07/Dec/25 $${Formulate}\:{the}\:{differential} \\ $$$${equation}\:{of}\:{the}\:{solution} \\ $$$$\left({a}\right){y}={Ae}^{{bx}+\mathrm{1}} \\ $$$$\left({b}\right){y}={A}\mathrm{sin}\:{x}+{B}\mathrm{cos}\:{x} \\ $$$$ \\ $$ Answered by mr W last…