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Author: Tinku Tara

let-f-0-1-R-prove-that-x-0-x-1-x-2-0-1-such-that-f-x-0-x-0-2-f-x-1-2x-1-2-3f-x-2-

Question Number 140392 by mathdanisur last updated on 07/May/21 $${let}\:{f}:\left[\mathrm{0};\mathrm{1}\right]\rightarrow\mathbb{R},\:{prove}\:{that}\:\exists{x}_{\mathrm{0}} ,{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} \in\left(\mathrm{0};\mathrm{1}\right) \\ $$$${such}\:{that}\:\:\frac{{f}\left({x}_{\mathrm{0}} \right)}{{x}_{\mathrm{0}} ^{\mathrm{2}} }+\frac{{f}\left({x}_{\mathrm{1}} \right)}{\mathrm{2}{x}_{\mathrm{1}} ^{\mathrm{2}} }=\mathrm{3}{f}\left({x}_{\mathrm{2}} \right) \\ $$ Terms…

Is-it-possible-to-combine-2cos-90-x-cos-180-x-into-a-form-of-a-cos-b-x-c-2cos-pi-2-x-cos-pix-a-cos-bx-c-

Question Number 74853 by Raxreedoroid last updated on 01/Dec/19 $$\mathrm{Is}\:\mathrm{it}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{combine}\:\mathrm{2}{cos}\left(\mathrm{90}°{x}\right)+{cos}\left(\mathrm{180}°{x}\right) \\ $$$$\mathrm{into}\:\mathrm{a}\:\mathrm{form}\:\mathrm{of}\:\:{a}\centerdot{cos}\left({b}\centerdot{x}+{c}\right) \\ $$$$\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{2}}{x}\right)+{cos}\left(\pi{x}\right)\overset{?} {=}{a}\centerdot{cos}\left({bx}+{c}\right) \\ $$ Commented by mr W last updated on 01/Dec/19…

Question-140384

Question Number 140384 by Willson last updated on 07/May/21 Answered by benjo_mathlover last updated on 07/May/21 $$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{x}^{\mathrm{p}} +\mathrm{1}\right)^{\mathrm{n}} \left(\mathrm{x}^{\mathrm{q}} +\mathrm{1}\right)^{\mathrm{m}} −\mathrm{1}}{\mathrm{x}}\:= \\ $$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{nx}^{\mathrm{p}}…