Numerical and Graphical Approximations (a) Use the Maclaurin polynomials P 1 ( x ) , P 3 ( x ) , and P 5 ( x ) for f ( x ) = sin x to complete the table. X 0 0.25 0.50 0.75 1 sin x 0 0.2474 0.4794 0.6816 0.8415 P 1 ( x ) P 3 ( x ) P 5 ( x ) (b) Use a graphing utility to graph f ( x ) = sin x and the Maclaurin polynomials in part (a). (c) Describe the change in accuracy of a polynomial approximation as the distance from the point where the polynomial is centered increases.
Numerical and Graphical Approximations (a) Use the Maclaurin polynomials P 1 ( x ) , P 3 ( x ) , and P 5 ( x ) for f ( x ) = sin x to complete the table. X 0 0.25 0.50 0.75 1 sin x 0 0.2474 0.4794 0.6816 0.8415 P 1 ( x ) P 3 ( x ) P 5 ( x ) (b) Use a graphing utility to graph f ( x ) = sin x and the Maclaurin polynomials in part (a). (c) Describe the change in accuracy of a polynomial approximation as the distance from the point where the polynomial is centered increases.
Solution Summary: The author explains that the Maclaurin polynomial for f is p_n(x)=f' (0 )x+
sin(x)
[²√(x² - 4x² + (1+x23²) dx = ²
A) True
B) False
b) Differentiate the function below with respect to x.
sin(-5+x)
4-8x
f(x) =
Note:
=
In Text mode the correct syntax is, say
• In Symbolic mode the correct syntax is, say
(6cos(5+6x)*(4+6x)-6sin(5+6x))/(4+6x)^2. Take note of the outer brackets in numerator.
6 cos(5+6x)+(4+6x)-6 sin(5+6x)
(4+6x)2
ƒ'(x) =
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