What is the limit of the function (sin2x-sin6x)/4x, x-->0?

Expert Answers

An illustration of the letter 'A' in a speech bubbles

We have to find the value of lim x-->0 [(sin 2x - sin 6x) / 4x]

We see that substituting x = 0 at this stage gives an indeterminate form 0/0.

So we use l'Hopital's rule and substitute the numerator and the denominator with their derivatives.

=> lim x-->0 [(2*cos 2x - 6* cos 6x) / 4]

substituting x = 0 here, we get (2 - 6)/4 = -1

The required value of lim x-->0 [(sin 2x - sin 6x) / 4x] = -1

See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team