Category: Relation and Functions

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…

Question Number 57410 by Abdo msup. last updated on 03/Apr/19 $$find{lim}_{x\to 1}\frac{sin(x^5+x-2)}{x-1}$$ Commented by maxmathsup by imad last updated on 04/Apr/19 $${in}\:{this}\:{case}\:{its}\:{beter}\:{to}\:{use}\:{hospital}\:{theorem}…

Question Number 57406 by Abdo msup. last updated on 03/Apr/19 $$letf\left(x\right)=\frac{x}{\sqrt{1+x^2}}+cos\left(\pi x\right)$$$$1)provethatf\left(x\right)=0haveasolurion\alpha inside]0,1[$$$$2)usenewtonmethodtofindaapproximate$$$$valueof\alpha .$$ Commented by kaivan.ahmadi last updated…