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Question-131027

Question Number 131027 by Algoritm last updated on 31/Jan/21 Answered by mathmax by abdo last updated on 31/Jan/21 $$\mathrm{cos}^{\mathrm{2m}} \mathrm{x}\:=\left(\frac{\mathrm{e}^{\mathrm{ix}} +\mathrm{e}^{−\mathrm{ix}} }{\mathrm{2}}\right)^{\mathrm{2m}} \:=\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2m}} }\sum_{\mathrm{k}=\mathrm{0}} ^{\mathrm{2m}}…

d-dx-or-

Question Number 131007 by Study last updated on 31/Jan/21 $$\frac{{d}}{{dx}}\left(\infty\right)=?\:\:\:\:\:{or}\:\:\:\left(\infty\right)'=? \\ $$ Answered by Boucatchou last updated on 31/Jan/21 $$\infty\:{is}\:{unknown},\:{so}\:\:{they}\:\:{can}'{t}\:\:{do}\:\:{such}\:\:{operations}.. \\ $$ Answered by MJS_new…

10-x-x-1000-x-

Question Number 65446 by LPM last updated on 30/Jul/19 $$\:\:\:\:\mathrm{10}^{\mathrm{x}} \:=\:\mathrm{x}^{\mathrm{1000}} \:\Rightarrow\:\mathrm{x}=? \\ $$ Commented by MJS last updated on 30/Jul/19 $${a}^{{x}} ={x}^{{b}} \\ $$$${x}\mathrm{ln}\:{a}\:={b}\mathrm{ln}\:{x}…