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Author: Tinku Tara

Use-De-Moivre-s-theorem-to-prove-that-r-0-cos-rx-1-2-and-find-a-value-or-expression-for-r-0-sin-rx-assume-that-this-two-series-were-convergent-

Question Number 136582 by physicstutes last updated on 23/Mar/21 $$\mathrm{Use}\:\mathrm{De}'\mathrm{Moivre}'\mathrm{s}\:\mathrm{theorem}\:\mathrm{to}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{cos}\:{rx}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{find}\:\mathrm{a}\:\mathrm{value}\left(\mathrm{or}\:\mathrm{expression}\right)\:\mathrm{for}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\mathrm{sin}\:{rx} \\ $$$$\mathrm{assume}\:\mathrm{that}\:\mathrm{this}\:\mathrm{two}\:\mathrm{series}\:\mathrm{were}\:\mathrm{convergent}. \\ $$ Answered by Ar Brandon last…

if-x-1-x-1-3x-x-2-ax-2-bx-c-then-a-b-c-

Question Number 5507 by Kasih last updated on 17/May/16 $${if}\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}\:{then}\:{a}=?\:{b}=?\:{c}=? \\ $$ Answered by Rasheed Soomro last updated on 17/May/16 $$\:\left({x}−\mathrm{1}\right)\:\left({x}+\mathrm{1}\right)\:+\mathrm{3}{x}+{x}^{\mathrm{2}} ={ax}^{\mathrm{2}} +{bx}+{c}…

if-the-degree-of-the-polynomial-p-x-is-less-than-the-degree-of-q-x-then-f-x-p-x-q-x-is-called-a-rational-function-

Question Number 5505 by Kasih last updated on 17/May/16 $${if}\:{the}\:{degree}\:{of}\:{the}\:{polynomial}\:{p}\left({x}\right)\:{is}\:{less}\:{than} \\ $$$${the}\:{degree}\:{of}\:{q}\left({x}\right)\:{then}\:{f}\left({x}\right)=\frac{{p}\left({x}\right)}{{q}\left({x}\right)}\:{is}\:{called}\:{a}\:.\:.\:.. \\ $$$${rational}\:{function} \\ $$$$ \\ $$ Commented by Rasheed Soomro last updated on…