The linear approximation at x=0 to sin(8x) is L(x)= A+Bx where A = B =

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Given `f(x)=sin(8x)` , find the linear approximation at x=0:

(1) f(0)=0

(2) `f'(x)=8cos(8x)` . This is the slope of the line tangent to f(x) at x.

(3) `f'(0)=8` This is the slope of the tangent line at x=0

(4) y-0=8(x-0) or y=8x is the line tangent to f(x) at (0,0); this is the linear approximation to f(x).

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