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Exam 2-Take Home - Exam 2 Take Home Name(last Last Name...

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Exam 2 – Take Home Name: ____________, _____________ (last) (first) Last Name f ( x ) Graph of f ( x ) Graph of f ( x ) Evaluate A x e x 2 1 ) 2 ln( 1 lim 2 - - - x x x B–C x e –2 x x x x ln 1 lim 0 + + D–H x e x /2 x x x / 1 0 ) (cos lim K-M x e x 2 /2 x x x ) 2 (sin lim 0 N–O x e x 2 /4 x x x 2 0 ) (tan lim P–R x 2 e x 1 0 ) / 1 ( lim - x e x x S-Y x 2 e –2 x ) 1 ln( ) 1 ( lim 1 - - + x x x Do them according to your last name: 1. Trapezoidal Rule (First 3 Columns) a) Use n = 5 to approximate the area of your region by Trapezoidal Rule from x = 0 to x = 5. [Hint: you must find h 0 , h 1 , h 2 , h 3 , h 4 , and h 5 first] b) Use the graph of f ( x ) to get K first and then use it to find the maximum error can be made, i.e., find | E T max |. c) Find the exact area of the region, i.e., evaluate your integral. [Hint: some need u -substitution, while others need integration by parts.] d) Find the actual error made, i.e., | E T act | e) Is your actual error less than the maximum error? [Note: Round all calculations to 4 decimal places.] 2. L’Hospital’s Rule (Last Column) a) Identify the indeterminate form first. b) Manipulate it to [0/0] or [∞/∞] so that you can use the l’Hospital’s rule to evaluate the limit.
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