Question

Limit X --> 0 sin(7x)/sin(2x)

Answer 1

could u use L hopital rule?

Answer 2

using L'hopital's rule:\[\lim_{x \rightarrow 0}\ \frac{ \frac{ d }{ dx }(\sin7x) }{\frac{ d }{dx }(\sin7x) }=\lim_{x \rightarrow 0}\ \frac{ 7\cos7x }{2\cos2x}\]
\[\frac{ 7 }{ 2 }\frac{ \lim_{x \rightarrow 0 } \cos7x}{ \lim_{x \rightarrow 0} \cos2x }=\frac{ 7\cos0 }{ 2\cos0 }=\frac{ 7 }{ 2 }\]

Answer 3

**sorry first line\[\lim_{x \rightarrow 0}\frac{ \frac{ d }{ dx }\sin7x }{ \frac{ d }{ dx }\sin2x }\]

Answer 4

\[\lim_{x \rightarrow0}\frac{ \sin 7x }{\sin 2x }=\frac{ \lim_{x \rightarrow 0}\frac{ \sin 7x }{ 7 }*7 }{\lim_{x \rightarrow 0} \frac{\ \sin 2x }{ 2 }*2 }\]
\[=\frac{ 7 }{ 2}*\frac{ 1 }{1 }=\frac{ 7 }{ 2 }\]