P MT 11 sln

P MT 11 sln - Math 1A Calculus Fall 2006 Prof Haiman...

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Unformatted text preview: Math 1A Calculus Fall, 2006 Prof. Haiman Practice Exam for Midterm 1—Solutions 1. Find the domain and range of the function f ( x ) = 1 ( x- 2) 2 . The domain is x 6 = 2. The range is (0 , ∞ ), since f ( x ) is always positive, approaches 0 for large x , and approaches ∞ for x approaching 2. 2. Express the function u ( t ) = cos t 1 + cos t as a composite f ◦ g of two other functions. u = f ◦ g for f ( t ) = t/ (1 + t ), g ( t ) = cos t . 3. An exponential function f ( x ) = Ca x has f (1) = 10 and f (3) = 40. Find the constants C and a . f (3) /f (1) = a 3 /a = a 2 = 4, so a = 2. Plugging in x = 1 shows that C = 5. 4. Evaluate the limit, if it exists (possibly as an infinite limit). lim x → 3 √ x + 1- 2 x- 3 . lim x → 3 √ x + 1- 2 x- 3 = lim x → 3 x + 1- 4 ( x- 3)( √ x + 1 + 2) = lim x → 3 1 √ x + 1 + 2 = 1 / 4 . 5. Evaluate the limit, if it exists (possibly as an infinite limit)....
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P MT 11 sln - Math 1A Calculus Fall 2006 Prof Haiman...

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