18.01 PROBLEM SET 6

Hand in to Room 2-108 by 1:00 pm Wednesday, April 24.

The due date and time are absolute. Late homeworks are accepted until the solutions are posted, but the score will be multiplied by 1/2.

Everything included here may be used later. You do not need to memorize the proofs, but you need to know the facts.

1. 293/1, 5, 16. F.3/F4. 299/1, 9, 15. 305/17, 22, 23. (10 points)

2. Read section 10.9 from your book. Then

(a) State the trapezoidal rule and Simpson’s rule for n = 4.

(b) Compute the value of

4 · ∫_{0}^{1} \frac{dx}{1 + x^{2}} .

(c) Use both of these rules to find rational numbers that approximate the value

of π. Which approximation is more accurate? (15 points)

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