Category: Relation and Functions

Question Number 53961 by maxmathsup by imad last updated on 27/Jan/19 $$let\phi \left(x\right)=\frac{arctan\left(2x\right)}{1-x^2}$$$$1)calculate{\phi }^{\left(n\right)}\left(x\right)$$$$2)calculate{\phi }^{\left(n\right)}\left(0\right)anddevelpp\phi atintegrserie$$ Commented by maxmathsup by…

Question Number 53957 by maxmathsup by imad last updated on 05/Feb/19 $$letf\left(x\right)=arctan(1+2x)$$$$1)calculate{f}^{\left(n\right)}\left(x\right)then{f}^{\left(n\right)}\left(0\right)$$$$2)developpfatintegrserie.$$$${we}\:{have}\:{f}^{'} \left({x}\right)=\frac{\mathrm{2}}{\mathrm{1}+\left(\mathrm{1}+\mathrm{2}{x}\right)^{\mathrm{2}} }\:\Rightarrow\:{f}^{\left({n}\right)} \left({x}\right)\:=\mathrm{2}\:\left\{\frac{\mathrm{1}}{\left(\mathrm{2}{x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}}\right\}^{\left({n}−\mathrm{1}\right)} \:\:{with}\:{n}>\mathrm{0}…

Question Number 119391 by Don08q last updated on 24/Oct/20 $$\mathrm{Given}\mathrm{that}f(x-3)=x^2-12x+41$$$$\mathrm{find}\mathrm{an}\mathrm{explicit}\mathrm{expression}\mathrm{for}f\left(x\right)$$$$$$$$pleaseIneedtheprocedure$$ Answered by bemath last updated on…

Question Number 53781 by maxmathsup by imad last updated on 25/Jan/19 $${calculateA}_n=\sum _{n=1}^{\mathrm{\infty }}{x}^{n}cos\left(n\theta \right)and{B}_n=\sum _{n=1}^{\mathrm{\infty }}{x}^{n}sin\left(n\theta \right)$$ Commented by maxmathsup…

Question Number 53779 by maxmathsup by imad last updated on 25/Jan/19 $$\mathrm{\Sigma }{u}_{n}isaconvergentserie(u_n>0)findnatureoftheserie$$$$1)\mathrm{\Sigma }\frac{\sqrt{u_n}}{n}$$$$2)\mathrm{\Sigma }\frac{u_n}{1+u_n}$$ Terms of…