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Category: Differentiation

Question-147346

Question Number 147346 by mnjuly1970 last updated on 20/Jul/21 Answered by qaz last updated on 20/Jul/21 $$\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \left(\mathrm{1}−\mathrm{sin}\:\mathrm{x}\right)^{\mathrm{n}} \mathrm{sin}\:\mathrm{xd}\left(\mathrm{sin}\:\mathrm{x}\right) \\ $$$$\Rightarrow\mathrm{a}_{\mathrm{n}} =\mathrm{2}\int_{\mathrm{0}} ^{\mathrm{1}}…

Question-147209

Question Number 147209 by alcohol last updated on 18/Jul/21 Commented by Ar Brandon last updated on 19/Jul/21 $$\mathrm{1}.\int_{−\mathrm{a}} ^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}=\int_{−\mathrm{a}} ^{\mathrm{0}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx}+\int_{\mathrm{0}} ^{\mathrm{a}} \mathrm{f}\left(\mathrm{x}\right)\mathrm{dx} \\…

Question-147135

Question Number 147135 by puissant last updated on 18/Jul/21 Answered by gsk2684 last updated on 18/Jul/21 $${let}\:{y}={x}^{{x}^{{x}^{.} } } \:{then}\:{y}={x}^{{y}} \\ $$$$\mathrm{ln}\:{y}\:=\:{y}\:\mathrm{ln}\:{x} \\ $$$$\frac{\mathrm{1}}{{y}}\:\frac{{dy}}{{dx}}={y}\:\frac{\mathrm{1}}{{x}}\:+\:\frac{{dy}}{{dx}}\:\mathrm{ln}\:{x} \\…

f-x-x-2-e-x-f-100-0-

Question Number 81439 by jagoll last updated on 13/Feb/20 $$\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}} \:\mathrm{e}^{\mathrm{x}} \\ $$$$\mathrm{f}^{\left(\mathrm{100}\right)} \left(\mathrm{0}\right)\:=\:? \\ $$ Commented by john santu last updated on 13/Feb/20 $$\Rightarrow\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{x}^{\mathrm{2}}…

Montrer-que-k-0-2n-1-cos-2n-k-2n-nC-2n-n-2-2n-1-

Question Number 146924 by Willson last updated on 16/Jul/21 $$\boldsymbol{\mathrm{Montrer}}\:\boldsymbol{\mathrm{que}} \\ $$$$\underset{\boldsymbol{{k}}=\mathrm{0}} {\overset{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} {\sum}}\boldsymbol{{cos}}^{\mathrm{2}\boldsymbol{{n}}} \left(\boldsymbol{\theta}+\frac{\boldsymbol{{k}\pi}}{\mathrm{2}\boldsymbol{{n}}}\right)=\:\frac{\boldsymbol{{nC}}_{\mathrm{2}\boldsymbol{{n}}} ^{\boldsymbol{{n}}} }{\mathrm{2}^{\mathrm{2}\boldsymbol{{n}}−\mathrm{1}} } \\ $$ Answered by mindispower last updated…