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Section 4: Lagrange Remainder

Section 4: Lagrange Remainder. Remainder ( R n (x ) ) : the difference between the actual value of the function and the approximation. Lagrange Error Bound.

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Section 4: Lagrange Remainder

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  1. Section 4: Lagrange Remainder

  2. Remainder(Rn(x)): the difference between the actual value of the function and the approximation.

  3. Lagrange Error Bound

  4. Ex 1: a) Use a 6th order Maclaurin polynomial to approximate cos(2). b) Use Lagrange Error Bound to write the upper and lower bounds for your estimate of cos(2).

  5. Ex 2: a) Use a 3rd degree Maclaurin polynomial to approximate . b) How much error?c) What degree polynomial would you need to have an error less than 0.001?

  6. Ex 3: a) Use a 3rd order Taylor polynomial centered at x=1 to approximate ln(1.5). b) Estimate the error in your answer.

  7. Section 4 WS#1 – 19 odds, 26skip #9

  8. Let a) Use a 0th order Maclaurin polynomial to approximate . b) Find R0(1).c) Find z.

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