Student number Name [SURNAME(S), Givenname(s)] MATH 100, Section 110 (CSP) Week 8: Marked Homework Assignment Due: Thu 2010 Nov 04 14:00 HOMEWORK SUBMITTED LATE WILL NOT BE MARKED 1. Find the nth-degree Taylor polynomial of f at a if: (a) f (x) = x5/2 , a = 4, n = 2; (b) f (x) = √ x, a = 4, n = 3; (c) f (x) = cos x, a = π3 , n = 5. 2. Use Taylor’s Formula with Remainder to find an upper bound on the absolute value of the error made when linear approximation at 4 is used to estimate (3.9)5/2 . Also determine (with justification) whether the linear approximation is greater than or less than the exact value (3.9)5/2 . 3. Use Taylor’s Formula with Remainder to find an upper bound on the absolute value √ of the error made when the 2nd degree Taylor polynomial at 4 is used to√estimate 4.2. Is the error positive or negative? Is T2 (4.2) greater than or less than 4.2? Then use a calculator to compute the actual error. 4. Determine what degree Taylor polynomial of cos x at π/3 is needed to guarantee that the Taylor polynomial approximation of cos 69o is accurate to within 0.000005 = 5 × 10−6 . 5. Determine what degree of Maclaurin polynomial of ln(1 + x) is needed to estimate ln 1.4 to within 0.001. 6. Find the absolute maximum and the absolute minimum of each of the following functions on the indicated intervals: (a) f (x) = 8x5 − 5x4 − 20x3 , (b) g(x) = x1/3 − x2/3 , (c) h(t) = t 2/3 2 (t − 2) , −1 ≤ x ≤ 2. −1 ≤ x ≤ 1. −1 ≤ t ≤ 1.