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