Question

Determine the tangent line approximation for ?(?) = 2sin(? ? ) at the point (0, 2???1)

Answer 1

we know that tangent line approximation for the function f(x) at the point (a,f(a)) is given by,

we have a point (a,f(a)) = (0,2sin1) hence put a = 0 we can write,

   -----------------------------------------------------------------1)

we have f(x) = 2sin(e^x) hence,

we have f(x) = 2sin(e^x) hence,

Hence,

we have f(0) = 2sin(1) and f'(0) = 2cos(1) put them in equation 1) we can say that tangent line approximation for f(x) = 2sin(e^x) at the point (0, 2sin1) is given by,