Question

Find lim x approaches 0 of sin(2x)/x using only sanwich thorem or limit properties. Thnaks

Answer 1

\[\frac{\sin(2x)}{x}=2\frac{\sin(2x)}{2x}\]

Answer 2

so?

Answer 3

can go further

Answer 4

\[\lim_{x\to0}\frac{\sin(2x)}{x}=\lim_{x\to0}2\frac{\sin(2x)}{2x}=2\cdot 1=2\]

Answer 5

how do we know that sin(2x)/2x is 1?

Answer 6

its called ''important limit''