20b_04f_2e

# 20b_04f_2e - Rule with 100 intervals to approximate the...

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Math 20B Second Midterm 40 points November 15, 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. One sheet of NOTES is allowed. You must show your work to receive credit. 1. (5 points each) Consider the curve in the Frst quadrant (that is, x 0 and y 0) described by x 4 + y 2 = 1. Write down, but do not evaluate integrals for the following: (a) the length of the curve (b) the surface area when the curve is rotated about the x -axis. 2. (4 points each) An integral I = i b a f ( x ) dx was approximated using the Trapezoidal Rule with 25 intervals. The error was somehow estimated to be about 0.08. Answer the following. You do not need to give reasons. (a) What is a reasonable estimate for the error if we decide to use the Trapezoidal
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Unformatted text preview: Rule with 100 intervals to approximate the integral I ? (b) What is a reasonable estimate for the error if we decide to use the Midpoint Rule with 25 intervals to approximate the integral I ? 3. (5 points each) The complex number z has absolute value 2 and argument 3 π/ 4. Do each of the following and do not leave trig functions in your answers. (a) ±ind the Cartesian form of z (that is, x + iy ). (b) ±ind the polar form of all cube roots of z (that is, r and θ ). 4. (6 points) ±ind y (3), given that y ′ ( x ) = 2 xy and y (0) = 2. 5. (6 points) Evaluate I 2 x 2 dx x 2-1 . END O± EXAM...
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