Use a graph to estimate:

Question

Lim x-> 0 of sin(8x)/x

when x is measured in degrees.

Answer 1

change it to radians.

lim sin(8*2PI/360 x)/(2PI/360 x) x in radians, lim as x>>>0

lim sin(16PI/360 x)/x * 360/2PI

using L'Hopitals rule, to make certain..

lim= cos(16PI/360 x) * 16PI/360 /1 * 360/2PI

= 1*16PI*360/360*2PI= 8

another way to do it. Let u=8x
du=8dx

lim sin u/u/8= 8