Category: Relation and Functions

Question Number 57488 by Abdo msup. last updated on 05/Apr/19 $$let{A}_n={\int }_0^n\frac{t\left[t\right]}{3+t^2}dt$$$$1)calculate{lim}_{n\to +\mathrm{\infty }}{A}_n$$$$2)findnatureif\mathrm{\Sigma }{A}_n$$ Commented by maxmathsup…

Question Number 122998 by benjo_mathlover last updated on 21/Nov/20 $$f:R\to R$$$$f\left(x\right)=\{\begin{array}{l}{x}^2+2mx-1;x⩽0\\ mx-1;x>0\end{array}$$$$iff\left(x\right)isone-onethenmlies$$$$ininterval$$$$\left(a\right)(-\mathrm{\infty },0)\left(c\right)(0,\mathrm{\infty })$$$$\left(b\right)(-\mathrm{\infty },0]\left(d\right)[0,\mathrm{\infty })$$ Terms of…

Question Number 57416 by Abdo msup. last updated on 03/Apr/19 $$letf\left(x\right)={\int }_{2x}^{4x}\frac{dt}{t^2-2t+3}$$$$1)findf\left(x\right)$$$$2)calculate{lim}_{x\to 0}f\left(x\right)and{lim}_{x\to +\mathrm{\infty }}f\left(x\right)$$ Commented by maxmathsup…

Question Number 57414 by Abdo msup. last updated on 03/Apr/19 $$solve{y}^{\prime }=2y^2+yandy\left(o\right)=1$$ Commented by kaivan.ahmadi last updated on 03/Apr/19 $$firstwenoticetheintegral$$$$\int\frac{{dx}}{\mathrm{2}{x}^{\mathrm{2}} +{x}}=\int\frac{{dx}}{{x}\left(\mathrm{2}{x}+\mathrm{1}\right)}=…

Question Number 57412 by Abdo msup. last updated on 03/Apr/19 $$let{u}_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\dots +\frac{1}{\sqrt{n}}$$$$provethat\left(u_n\right)isdivdrgente.$$ Commented by maxmathsup by imad last updated on…