The linear approximation at x = 0 to sin ( 6 x ) is A + B x where A is: and where B is

Question

The linear approximation at  to  is  where  is:    and where  is

Answer 1

Hi,

he linear approximation at x=0 to sin(6x) is A+Bx where A is:    and where B is

First, f(x) = sin6x

Second , x = 0 -----> f(0) = sin (6*0) = 0 -----> point is ( 0 , 0 )

Third, f'(x) = 6 cox(6x)

Fourth, find slope -------> slope= m = f'( 0) = 6 cos( 0 *6 ) = 6

now you need to write equation of tangent line: y - 0 = 6 ( x - 0 ) ------> y = 6x now compare with A + Bx

you see A = 0 B = 6

I hope it works for you,

Minoo