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140Bmid2c - 1 Date Nov 5 2007 MATH 140B EXAMINATION 2 Print...

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1 Date: Nov 5, 2007 MATH 140B Print NAME: EXAMINATION 2 STUDENT NUMBER: FORM A There are 14 multiple choice questions each worth 5 points. The remaining 30 points are long answer questions on the last two pages. For each multiple choice answer, circle only one answer in your exam booklet and blacken the corresponding scantron sheet. The use of a calculator, cell phone, or any other electronic device is NOT permitted in this examination. The use of notes of any kind is NOT permitted during this exam. There are 15 problems on 10 numbered pages, including this cover page.
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2 [ 5 ] 1. Compute the value of lim x →∞ parenleftbigg 1 - x 3 2 x 3 - 4 x + 1 parenrightbigg A) -∞ , B) - 1 / 2, C) 1, D) + , E) none of the above. [ 5 ] 2. Compute the value of lim x →−∞ parenleftbigg - 3 x 5 + x + 1 x 3 - 2 parenrightbigg A) -∞ , B) - 3, C) 0, D) + , E) none of the above. [ 5 ] 3. Let y = f ( x ) be a differentiable function on an interval I. Suppose f ( c ) = 0 , x = c is the only critical point of f on I, and f ′′ ( c ) > 0 . Which of the following 2 statements are correct? i) f has a relative minimum at x = c. ii) f has an absolute minimum at x = c. A) i) only, B) ii) only, C) neither statement is correct, D) both statements are correct
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3 [ 5 ] 4. Given f ( x ) = x 4 + 4 x, which of the following 3 statements are correct? i) f ′′ ( x ) = 12 x 2 ii) f ′′ ( x ) = 0 when x = 0 . iii) There is a point of inflection at x = 0 . A) i) only, B) i) and ii) only, C) i) and iii) only, D) ii) and iii) only, E) all of the statements are correct. [ 5 ] 5. Use implicit differentiation to find the equation of the tangent line to the curve defined by xy 2 + 3 y = 1 at the point ( - 2 , 1) .
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