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

Question

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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!!