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Category: Relation and Functions

find-the-sequence-a-n-wich-verify-n-1-x-n-n-0-x-n-n-1-n-0-a-n-x-n-also-find-the-radius-of-this-serie-

Question Number 49961 by maxmathsup by imad last updated on 12/Dec/18 $${find}\:{the}\:{sequence}\:\left({a}_{{n}} \right)\:{wich}\:{verify}\: \\ $$$$\left(\sum_{{n}=\mathrm{1}} ^{\infty} \:{x}^{{n}} \right)\left(\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{\left(−{x}\right)^{{n}} }{{n}+\mathrm{1}}\right)=\sum_{{n}=\mathrm{0}} ^{\infty} \:{a}_{{n}} {x}^{{n}} \:\:{also}\:{find}\:{the}\:{radius}\:{of}\:{this}\:{serie}.…

1-simplify-A-n-1-2-i-3-n-1-2-i-3-n-2-smplify-B-n-1-2-3-n-1-2-3-n-n-integr-natural-

Question Number 49952 by maxmathsup by imad last updated on 12/Dec/18 $$\left.\mathrm{1}\right)\:{simplify}\:{A}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{2}+{i}\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−{i}\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$$\left.\mathrm{2}\right)\:{smplify}\:\:{B}_{{n}} =\frac{\mathrm{1}}{\left(\mathrm{2}+\sqrt{\mathrm{3}}\right)^{{n}} }\:+\frac{\mathrm{1}}{\left(\mathrm{2}−\sqrt{\mathrm{3}}\right)^{{n}} } \\ $$$${n}\:{integr}\:{natural}. \\ $$ Commented…

calculate-S-n-x-x-1-2-x-2-4-x-4-8-x-2-n-2-n-1-

Question Number 49810 by Abdo msup. last updated on 10/Dec/18 $${calculate}\: \\ $$$${S}_{{n}} \left({x}\right)=\left[\frac{{x}+\mathrm{1}}{\mathrm{2}}\right]\:+\:\left[\frac{{x}+\mathrm{2}}{\mathrm{4}}\right]\:+\left[\frac{{x}+\mathrm{4}}{\mathrm{8}}\right]+…\left[\frac{{x}+\mathrm{2}^{{n}} }{\mathrm{2}^{{n}+\mathrm{1}} }\right] \\ $$ Commented by maxmathsup by imad last updated…

solve-the-system-4-1-x-2-x-5-1-y-2-y-6-1-z-2-z-x-y-z-xyz-

Question Number 49809 by Abdo msup. last updated on 10/Dec/18 $${solve}\:{the}\:{system}\:\:\:\begin{cases}{\frac{\mathrm{4}\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{{x}}\:=\frac{\mathrm{5}\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }}{{y}}=\frac{\mathrm{6}\sqrt{\mathrm{1}+{z}^{\mathrm{2}} }}{{z}}}\\{{x}+{y}+{z}={xyz}.}\end{cases} \\ $$$$\left.\begin{matrix}{}\\{}\end{matrix}\right\} \\ $$ Commented by MJS last updated on 12/Dec/18…

let-f-x-e-x-x-1-1-calculate-f-n-o-and-f-n-1-2-developp-f-at-integr-serie-

Question Number 49804 by maxmathsup by imad last updated on 10/Dec/18 $${let}\:{f}\left({x}\right)\:=\frac{{e}^{−{x}} }{{x}+\mathrm{1}} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{f}^{\left({n}\right)} \left({o}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie}\:. \\ $$ Commented by Abdo msup.…

Equation-of-circle-touching-the-line-x-2-y-3-4-will-be-

Question Number 115261 by bobhans last updated on 24/Sep/20 $${Equation}\:{of}\:{circle}\:{touching}\:{the}\:{line}\: \\ $$$$\mid{x}−\mathrm{2}\mid+\mid{y}−\mathrm{3}\mid\:=\:\mathrm{4}\:{will}\:{be}\: \\ $$ Answered by john santu last updated on 24/Sep/20 $${centre}\:{of}\:{circle}\:{is}\:{a}\:{point}\:\left(\mathrm{2},\mathrm{3}\right) \\ $$$${with}\:{radius}\:=\:\frac{\mid\mathrm{2}+\mathrm{3}−\mathrm{9}\mid}{\:\sqrt{\mathrm{2}}}\:=\mathrm{2}\sqrt{\mathrm{2}}…

Given-f-x-sin2x-2cos2x-find-f-pi-4-hence-given-g-x-x-0-x-2-3x-x-2-2-x-3-for-a-total-range-of-0-x-3-sketch-the-graph-for-y-g-x-and-find-the-area-with-makes-with-the-x-axis

Question Number 49703 by Rio Michael last updated on 09/Dec/18 $${Given}\:{f}\left({x}\right)=\:{sin}\mathrm{2}{x}+\mathrm{2}{cos}\mathrm{2}{x} \\ $$$${find}\:{f}'\left(\frac{\pi}{\mathrm{4}}\right) \\ $$$${hence}\:{given}\:{g}\left({x}\right)\:=\:\begin{cases}{{x},\:\:\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}}\\{\mathrm{3}{x}−{x}^{\mathrm{2}} ,\:\:\mathrm{2}\leqslant{x}\leqslant\mathrm{3}}\end{cases} \\ $$$${for}\:{a}\:{total}\:{range}\:{of}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{3}\:\:{sketch}\:{the}\:{graph}\:{for}\:{y}={g}\left({x}\right) \\ $$$${and}\:{find}\:{the}\:{area}\:{with}\:{makes}\:{with}\:{the}\:{x}−{axis} \\ $$$${otherwise},\:{find}\:\:\:{the}\:{composite}\:{function}\:\:{gf}\:\:{in}\:{the}\:{range} \\ $$$$\mathrm{2}\leqslant{x}\leqslant\mathrm{3}. \\…