17. The following values of the function f(x) = sin x + cos x, are given 10° 20° 30° flx) 1.1585 1.2817 1.3660 Construct the quadratic Lagrange interpolating polynomial that fits the data. Hence, find f(n/12). Compare with the exact value.
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- By expanding (xh)2+(yk)2=r2, we obtain x22hx+h22ky+k2r2=0. When we compare this result to the form x2+y2+Dx+Ey+F=0, we see that D=2h,E=2k, and F=h2+k2r2. Therefore, the center and the length of a radius of a circle can be found by using h=D2,k=E2 and r=h2+k2F. Use these relationship to find the center and the length of the radius of each of the following circles. x2+y2+4x14y+49=0Suppose a table of values of f(x) = sin(x), 0 ≤ x ≤ 1.58, is to be constructed with the values of sin(x) given with a spacing of h. (a) If linear interpolation is used in this table, how small should h be in order for the interpolation error to be less than 10^-6? (b)If quadratic interpolation is used in this table, how small should h be in order for the interpolation error to be less than 10^-6?Part d) using values from b and c form the taylor's expression of y at x=0.5, truncated to include the first 2 terms