midterm2 prac

midterm2 prac - f(2 =-3 and f 00 x< 0 for all x then(a...

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Student name: Student PID: MATH 10A (Butler) Midterm 2, 5 March 2007 This test is closed book and closed notes, with the exception that you are allowed one 8 1 2 00 × 11 00 page of handwritten notes. You may use any shortcuts for derivatives unless explicitly stated otherwise. No calculator is allowed for this test. For full credit show all of your work (legibly!), unless otherwise specified. You do not need to simplify your answers any more than the question requires. 1. (8 points) Find the tangent line to the curve g ( x ) = ln( x 2 + 1) at x = - 1. 1 2 3 4 5 6 Σ
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2. (a) (2 points) Complete the following definition of the derivative for f ( x ): f 0 ( x ) = lim h 0 (b) (6 points) Using the definition for the derivative given above, find f 0 ( x ) for f ( x ) = 4 x 2 - 3 x . [Remember to show all of your work!!]
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3. Let f ( t ) = te - t . (a) (4 points) When is f ( t ) increasing? (b) (4 points) When is f ( t ) concave down?
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4. (MULTIPLE CHOICE QUESTIONS, 3 points each). Write your answer in the space provided. There is no partial credit for incorrect answers. If f (2) = 7 and
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Unformatted text preview: f (2) =-3 and f 00 ( x ) < 0 for all x then (a) f (1) < 10. (b) f (1) = 10. (c) f (1) > 10. (d) there is not enough information to say anything about f (1). If f ( ω ) = e 3 π 100 then f ( ω ) is (a) e 3 π 100 . (b) 3 e 2 π 100 . (c) 100 e 3 π 99 . (d) 300 e 2 π 99 . (e) e 3 π 100 + 100 e 3 π 99 . (f) 3 e 2 π 100 + 100 e 3 π 99 . (g) none of the above. If f ( r ) = cosh(2 r ) then f (101) (0) (i.e., the 101st derivative evaluated at 0) is (a)-2 101 (b) 0 (c) 1 (d) 2 101 (e) none of the above. 5. Find the derivatives of the following functions (hint: it might be possible to simplify the function before taking the derivative): (a) (5 points) f ( x ) = cos 2 ( x 2 ) + tan 2 ( x 2 ) + sin 2 ( x 2 ) (b) (4 points) f ( x ) = y 4-2 y 2 + 1019 y + 3 y 6. (8 points) Find an expression for dy dx (i.e., dy dx = something involving y and/or x ) given that x + y = arctan( y ) ....
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midterm2 prac - f(2 =-3 and f 00 x< 0 for all x then(a...

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