MathPracticeFinal2

# MathPracticeFinal2 - Math 1A Spring 2008 Wilkening Sample...

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Math 1A, Spring 2008, Wilkening Sample Final Exam 2 You are allowed one 8 . 5 × 11 sheet of notes with writing on both sides. This sheet must be turned in with your exam. Calculators are not allowed. 0. (1 point) write your name, section number, and GSI’s name on your exam. 1. (3 points) give precise deﬁnitions of the following statements or expressions: (a) f ( x ) is neither even nor odd (b) R f ( x ) dx (c) R b a f ( x ) dx 2. (4 points) Show that the tangent lines to the curves y = x 3 and x 2 + 3 y 2 = 1 are perpendicular where the curves intersect. 3. (3 points) Evaluate Z 1 0 tan - 1 x 1 + x 2 dx . 4. If f is continuous and R 4 0 f ( x ) dx = 6, ﬁnd R 2 0 f (2 x ) dx . 5. (5 points) A right circular cone of height h and base radius R has a hole of radius r drilled through its center (from the tip to the center of the base). Find the volume of the solid that remains. 6. (5 points) Let f ( x ) = tanh - 1 (sin x ) and g ( x ) = ln | sec x + tan x | . Compute f 0 ( x ), g 0 ( x ), f ( ) and

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MathPracticeFinal2 - Math 1A Spring 2008 Wilkening Sample...

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