Consider the Taylor polynomial p.(r) of sin(2x) centered at r=0. a) Give an upper bound of...

Transcribed Image Text:

Consider the Taylor polynomial p.(r) of sin(2x) centered at r=0. a) Give an upper bound of the error when sin(2.r) is approximated by ps(r) on the interval [-/2, 1/2). b) Using p, (0.1) to approximate sin(0.2). Find the smallest n such that the approximation error is less than or equal to 10. (Hint: give an upper bound of the remainder on the interval [0,0.1] then use it to find the smallest n.) c) Compute ps(r). Find the largest interval (-6, 6] such that the approximation error is less than 105. Graph the function sin(2x)-Pa(z) on that interval to confirm your answer. Consider the Taylor polynomial p.(r) of sin(2x) centered at r=0. a) Give an upper bound of the error when sin(2.r) is approximated by ps(r) on the interval [-/2, 1/2). b) Using p, (0.1) to approximate sin(0.2). Find the smallest n such that the approximation error is less than or equal to 10. (Hint: give an upper bound of the remainder on the interval [0,0.1] then use it to find the smallest n.) c) Compute ps(r). Find the largest interval (-6, 6] such that the approximation error is less than 105. Graph the function sin(2x)-Pa(z) on that interval to confirm your answer.