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1124worksheet2

# 1124worksheet2 - f is continuous and f(3 = 0(a Sketch a...

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Polytechnic Institute of NYU MA 1124 Worksheet 2 Print Name: Signature: ID #: Instructor/Section: Directions: Show all your work for every problem. Problem Possible Points 1 12 2 16 3 12 4 12 5 12 6 12 7 12 8 12 Total 100

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Your signature: (1) Let Z b a f ( x ) dx = 5 , Z b a ( f ( x )) 2 dx = 8 , Z b a g ( t ) dt = - 3 and Z b a ( g ( t )) 2 dt = 9. Find the integrals (a) Z b a ( f ( x ) + g ( x )) dx (b) Z a b f ( z ) dz (c) Z a b (( f ( x )) 2 - ( g ( x )) 2 ) dx (d) Z b a ( f ( x )) 2 dx - Z b a f ( x ) dx 2 (e) Z a b ( g ( x ) + ( f ( x )) 2 ) dx (f) Z b +3 a +3 f ( x - 3) dx
Your signature: (2) Find Z 6 3 f ( x ) dx . (a) f ( x ) is odd and Z 6 - 3 f ( x ) = 3 dx (b) f ( x ) is even, Z 3 - 3 f ( x ) dx = 5, and Z 6 - 6 f ( x ) dx = 18 (c) Z 6 3 (5 f ( x ) + 4) dx = 21 (d) Z 4 3 3 f ( x ) dx = 9 and Z 4 6 f ( x ) = 5

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Your signature: (3) (a) If f ( x ) is odd and Z 7 - 3 f ( x ) dx = 20, find Z 3 7 f ( x ) dx . (b) If f ( x ) is even and Z 6 - 6 ( f ( x ) - 4) dx = 102, find Z 2 0 f (3 x ) dx .
Your signature: (4) (a) The average value of f ( x ) equals 10 for 1 x 7, and equals 8 for 7 x 12. What is the average value of f ( x ) for 1 x 12? (b) If the average value of f ( x ) on the interval 2 x 7 is 8, find Z 7 2 (5 f ( x )+5) dx .

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Your signature: (5) Assume f 0 ( x ) is given by following graph. Suppose

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Unformatted text preview: f is continuous and f (3) = 0. (a) Sketch a graph of f ( x ) (b) What is the average value of f ( x ) on [0 , 7]? Your signature: (6) The graph f 00 is given in the following ﬁgure. Assume that f (0) = 0 and f (0) = 0. Decide at which of the labeled x-values: (a) f ( x ) is greatest. (b) f ( x ) is least. (c) f ( x ) is greatest. (d) f ( x ) is least. (e) f 00 ( x ) is greatest. (f) f 00 ( x ) is least. Your signature: (7) Sketch a graph of an antiderivative, H ( t ), of h ( t ) satisfying H (0) = 12. Label each critical point of H ( t ). Your signature: (8) The following is a graph of g ( x ). (a) Find Z 12 3 g ( x ) dx (b) If g (3) = 4, what is g (12)?...
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