Part I. No Calculators
You may not have a calculator while this part of the test is in your posession. When you are through with this part, hand it in. Then you may work on the rest of the test using a calculator.
x | 0.0 | .25 | .50 | .75 | 1.00 | 1.25 | 1.50 | 1.75 | 2.00 |
f(x) | 0.0 | 1.492 | 2.08 | 2.48 | 2.75 | 2.92 | 3.00 | 2.98 | 2.86 |
We want to estimate .
a) Find the midpoint estimate with 4 subdivisions, MID(4).
b) You can easily calculate that LEFT(4) = 3.915 and RIGHT(4) = 5.345. Find the trapezoid and Simpson's estimates TRAP(4) and SIMP(4).
c) Verify that the function f(x) is concave down on the interval [0,2] by plotting points or by using numerical calculations.
d) Explain why your value of SIMP(4) must be approximately within 0.33 of the exact value of the integral. ( Hint: How far apart are your values for TRAP(4) and MID(4)?)
b) If only one decimal is correct in each number
given above for LEFT(5) and MID(5),
how many decimals you predict will be correct in
LEFT(50) and MID(50) ? Explain.