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Question Number 12492 by shardon last updated on 23/Apr/17
this is calculus   evaluate lim_(x→0) ((sin3xsin5x)/(7x^2 ))
$${this}\:{is}\:{calculus}\: \\ $$$${evaluate}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{sin}\mathrm{3}{xsin}\mathrm{5}{x}}{\mathrm{7}{x}^{\mathrm{2}} } \\ $$
Commented by shardon last updated on 23/Apr/17
what happen to the x^2
$${what}\:{happen}\:{to}\:{the}\:{x}^{\mathrm{2}} \\ $$
Answered by mrW1 last updated on 23/Apr/17
=lim_(x→0)  ((sin 3x )/(3x))×((sin 5x)/(5x))×((3×5)/7)  =1×1×((15)/7)=((15)/7)
$$=\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{3}{x}\:}{\mathrm{3}{x}}×\frac{\mathrm{sin}\:\mathrm{5}{x}}{\mathrm{5}{x}}×\frac{\mathrm{3}×\mathrm{5}}{\mathrm{7}} \\ $$$$=\mathrm{1}×\mathrm{1}×\frac{\mathrm{15}}{\mathrm{7}}=\frac{\mathrm{15}}{\mathrm{7}} \\ $$
Answered by Joel577 last updated on 24/Apr/17
lim_(x→0)  ((sin 3x)/(7x)) . ((sin 5x)/x)  = (3/7) . 5 = ((15)/7)
$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{3}{x}}{\mathrm{7}{x}}\:.\:\frac{\mathrm{sin}\:\mathrm{5}{x}}{{x}} \\ $$$$=\:\frac{\mathrm{3}}{\mathrm{7}}\:.\:\mathrm{5}\:=\:\frac{\mathrm{15}}{\mathrm{7}} \\ $$

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