Let f(x)= 1+ sin(x)
a) Find the Linear Approximation of f(x) at the (c,f(c)) = (0,1)
b) Evaluate both f(x) = 1+sin (x) and its linear approximation L(x) found in part(a) first as x = 0.01 and then at x=2.
c) For which x value in part (b) is f(x) approximated with greater accuracy.
I've tried to attempt the question but I'm not sure if I have the right answers. Please help!

Question

Let f(x)= 1+ sin(x)
a) Find the Linear Approximation of f(x) at the (c,f(c)) = (0,1) 
b) Evaluate both f(x) = 1+sin (x) and its linear approximation L(x) found in part(a) first as x = 0.01 and then at x=2.
c) For which x value in part (b) is f(x) approximated with greater accuracy.
I've tried to attempt the question but I'm not sure if I have the right answers. Please help!

anonymous · Answer

same as "find the equation for the line tangent to the graph"

anonymous · Answer

$$f(x)=1+\sin(x)$$
$$f'(x)=\cos(x)$$ $$m=f'(0)=\cos(0)=1$$ $(x_1,y_1)$ is $(0,1)$ equation of line is 
$$y-1=1(x-0)$$or more simpley 
$$y=x+1$$

anonymous · Answer

Okay, that's what I got for the first one too. What about the other too? Do I have to just substitute?

anonymous · Answer

The other two*

anonymous · Answer

yes. evidently your approximation will be good at $x=.01$ bur rather lousy at $x=2$ since this is the linear approximation at $x=0$

anonymous · Answer

Yup, that's what I got as well. Thank you SO much! :)

anonymous · Answer

yw