Question

find the linearization L(x) of F(x) at x=a
F(x)=e^x+sin(x) when a=0

Answer 1

this problem means "find the equation of the line tangent to the graph of
\[y=e^x+\sin(x)\] at the point
\[(0,1)\]

Answer 2

you need a point and a slope. the point you already have, it is (0,1) the slope you find by taking the derivative and then replacing x by 0 to find the slope at that point

Answer 3

\[f'(x)=e^x+\cos(x)\]
\[f'(0)=e^0+\cos(0)=2\] so the slope is 2 and the point is (0,1) use the point slope formula to find the equation of the line

Answer 4

so then you would get (y-1)=2(x-0) which would simplify to y=2x-1 which would be the same thing as L(x)=2x-1 which is the answer that is in the back of the book. thank you!!