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.