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2004 AP CALCULUS AB FREE-RESPONSE oussno'ns
CALCULUS AB
9 I. SECTION 11, Part B
t Time45 minutes
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.; No calculator ls allowed for these problems.
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4. Considcrthcmrvegivcn byixa + 4y2j=\7+3xy
Consider the di'écntial equittion g: = x (y -- 2). s
{a} Gill-the axes fovided, sketch a slope field for the given diffemnal equation at the twelxe points indicated-
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(b) While the 519p: eldin part (a is drgwn at only twelve points, it dcfihgd
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AP I Test (a) él N, N J #2843?
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I, Find the area of the region enclosed by the lines and curves.
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(a) x=r2_yz, x=0: A; I; GD-rCr) elk ((9-3 2: M l
1 1.:
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max ya: x .
(b) yi; I: i x2
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f-I.I31l
. For w
secant line?
(A) 0.248
(at
'1- ' .
; xzr and y = 2 is rotated nd the y-axis.
,f. (A) 0.296 0.592 (C) 2.42?
(£. bank account earns interest compoundedmcontinuously at
How many years, approximately,
(A)? (B) 9 (D) 33
36. The acceleration of
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6. If f is differentiable, We can use the line tangent to f at x = a to approximate values ~
f near 3': = a. Suppose this method always underestimates the corigect value???
then at x = a. fmust be
(A positive (B) increasing (C) d