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Examples / Error in Left- and Right-Hand Sums Examples
Error in Left- and Right-Hand Sums Exercises
Let f( x) = x 2. Calculate the following quantities.
Let f( x) = x 2 on the interval [0, 12]. How many rectangles must we use to guarantee that the right- and left-hand sums are within 10
of each other?
f( x) = 4 x + 6 on the interval [2, 8]. How many rectangles must we use to ensure that the left-hand sum is within 0.25 of the exact area between f and the x-axis on this interval?
f( x) = x 4 on the interval [-2 , -1]. For what values of n are LHS ( n) and RHS ( n) within 0.5 of each other on this interval?
Let f ( x) = cos( x) on the interval How large must n be to guarantee that LHS( n) is within 0.3 of the exact area between f and the x-axis on this interval?