Solve.A projectile is fired upward from the ground with an i…

Solve.A projectile is fired upward from the ground with an initial velocity of 500 feet per second. Neglecting air resistance, the height of the projectile at any time t can be described by the polynomial -16t2 + 500t. Find the height of the projectile at t = 4 seconds.

1. Let . (a)  [10 points] Find the third-order Taylor polyno…

1. Let . (a)   Find the third-order Taylor polynomial  for about and use it to approximate . Hint: You don’t need to simplify your final answer.  (b) Assume that  is used in order to approximate on . Then,  find an upper bound for the remainder or error involved in part (a). (c) Use the Taylor polynomial in part (a) to approximate

3. [25 points] Consider the function given by the values in…

3. Consider the function given by the values in the table below.                                                           0 2 4 Find the Lagrange form and Newton form of the interpolating polynomial What is the degree of your interpolating polynomial? Expand out the Lagrange and Newton forms to verify whether they agree with each other. Explain why.