Find the limit.

Question

Find the limit.

lim x→0 sin(2x)

5x

Answer 1

Well as both sin (2x) and 5x > 0, you need to use L'Hopitals rule (keep differentiating the numerator and denominator and evaluate at x=0 until denominator is non zero)

So lim x>0 sin (2x) / 5x = lim x > 0 2 cos (2x) / 5

Denominator is non zero so we can evaluate the limit which is 2 cos (0) / 5 = 2/5

Mike