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For the value sin(3.14) compute the values given with 0.01 by deciding on the right f(x) & a & evaluating L(x)=f(a)+f'(a)(x-a)?
Please show work so I can understand how to do this problem :)
1 Answer
- 4 years ago
3.14 is really close to pi, so sin(3.14) is going to be pretty close to sin(pi)
f(x) = sin(x)
f(pi) = sin(pi) = 0
f'(x) = cos(x)
f'(pi) = cos(pi) = -1
So we want a line with a slope of -1 that passes through (pi , 0)
y - 0 = -1 * (x - pi)
y = pi - x
x = 3.14
y = pi - 3.14
y = 0.00159265358....
Actual value of sin(3.14):
0.00159265291...
What do you think? Is that close enough?
