2. Let f(x) = sin r. (a) Hermite interpolating polynomial to approximate f(0.34) = sin 0.34....

Transcribed Image Text:

2. Let f(x) = sin r. (a) Hermite interpolating polynomial to approximate f(0.34) = sin 0.34. Use the following values and five-digit rounding arithmetic to construct the r| f(x) f'(x) 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 Determine an error bound for the approximation in part (a), and compare it to (b) the actual error. 2. Let f(x) = sin r. (a) Hermite interpolating polynomial to approximate f(0.34) = sin 0.34. Use the following values and five-digit rounding arithmetic to construct the r| f(x) f'(x) 0.30 0.29552 0.95534 0.32 0.31457 0.94924 0.35 0.34290 0.93937 Determine an error bound for the approximation in part (a), and compare it to (b) the actual error.