Use inequalities (12), (13), and (14) to find a number n of subintervals for (a) the midpoint approximation M n , (b) the trapezoidal approximation T n , and (c) Simpson’s rule approximation S n to ensure that the absolute error will be less than the given value. Exercise 2; 5 × 10 − 4
Use inequalities (12), (13), and (14) to find a number n of subintervals for (a) the midpoint approximation M n , (b) the trapezoidal approximation T n , and (c) Simpson’s rule approximation S n to ensure that the absolute error will be less than the given value. Exercise 2; 5 × 10 − 4
Use inequalities (12), (13), and (14) to find a number
n
of subintervals for (a) the midpoint approximation
M
n
,
(b) the trapezoidal approximation
T
n
,
and (c) Simpson’s rule approximation
S
n
to ensure that the absolute error will be less than the given value.
A small island is 2 miles from the nearest point P on the straight shoreline of a large lake. If a woman on the island can row a boat 2 miles per hour and can walk 3 miles per hour, where should the boat be landed in order to arrive at a town 9 miles down the shore from P in the least time? Let ?x be the distance between point P and where the boat lands on the lake shore.
Find the maximum error if the approximation 1 + x + x2/2 is used to approximate ex on the interval [0,2] - using Taylor's inequality.
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