The function F(x) = x2 - cos(π x) is defined on the
interval 0 ≤ x ≤ 1 radians. Explain how the Intermediate Value
Theorem shows that F(x) = 0 has a solution on the interval 0 < x
< .
For the given function f(x) = cos(x), let x0 = 0, x1 = 0.25, and
x2 = 0.5. Construct interpolation polynomials of degree at most one
and at most two to approximate f(0.15)
Let f(x) = sin(πx).
• x0 = 1,x1 = 1.25, and x2 = 1.6 are given. Construct Newton’s
DividedDifference polynomial of degree at most two.
• x0 = 1,x1 = 1.25,x2 = 1.6 and x3 = 2 are given. Construct
Newton’s Divided-Difference polynomial of degree at most three.
The function y(x, t) = (20.0 cm)
cos(πx - 17πt), with x
in meters and t in seconds, describes a wave on a taut
string. What is the transverse speed for a point on the string at
an instant when that point has the displacement y = +17.0
cm?
Number
Enter your answer in accordance to the question statement
Units
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statement
This answer has no units° (degrees)mkgsm/sm/s^2NJWN/mkg·m/s or
N·sN/m^2...
Find the least squares approximation of
f (x) = 7 + 3 cos(πx) over the
interval [−1, 1] by a polynomial of the form p(x)
= c0 + c1x +
c2x2.
(a)
Enter the polynomial p(x) into the answer box
below.
(b)
Find the mean square error of the approximation.