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A-lim-x-0-2x-4x-sint-t-dt-e-x-1-




Question Number 144403 by SOMEDAVONG last updated on 25/Jun/21
A=lim_(x→0) ((∫_(2x) ^(4x) ((sint)/t)dt)/(e^x −1)) =?
$$\mathrm{A}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{2x}} ^{\mathrm{4x}} \frac{\mathrm{sint}}{\mathrm{t}}\mathrm{dt}}{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}\:=? \\ $$
Answered by imjagoll last updated on 25/Jun/21
 A = lim_(x→0)  ((((sin 4x)/(4x))(4)−((sin 2x)/(2x))(2))/e^x )  A= ((4−2)/1)=2
$$\:\mathrm{A}\:=\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{4x}}\left(\mathrm{4}\right)−\frac{\mathrm{sin}\:\mathrm{2x}}{\mathrm{2x}}\left(\mathrm{2}\right)}{\mathrm{e}^{\mathrm{x}} } \\ $$$$\mathrm{A}=\:\frac{\mathrm{4}−\mathrm{2}}{\mathrm{1}}=\mathrm{2} \\ $$

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