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Midterm1 - (30 Points 3 Use Simpson’s rule to approximate...

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MATH 123 NAME: SUARAY SUMMER08 MIDTERM 1 (200 Points) You are allowed one hour and 30 minutes to complete this exam. You may use a calculator. You must show all work to get credit. There are six problems. 1. a. Find the volume of the solid obtained by rotating the region bounded by 1 about 2 , 1 , 0 , 2 = = = = = x x x y x y using the cylindrical shells (7.3) method, and sketch the region and solid. (15 Points) b. Verify your result for the above by using the washer (7.2) method. (15 Points)
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2. Suppose that 2J of work is needed to stretch a spring from its natural length of .3m to a length of .42m. How much work is needed to stretch it from .35m to .4m?
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Unformatted text preview: (30 Points) 3. Use Simpson’s rule to approximate the given integral with the specified value of n . (Round your answer to six decimal places.) Compare your results to the actual value to determine the error in the approximation. Is the actual error smaller than the theoretical bound? (30 Points) ∫ = 1 . 10 , n dx e x 4. ∫ + + 1 2 ) 1 ( 3 2 dx x x (40 Points) 5. Evaluate ∫ ∞-4 ) 2 ( dv v (40 Points) 6. Use the Comparison Theorem to determine whether h ( x ) dx 1 ∞ ∫ is convergent, where 6 1 ) ( x x x h + = . (30 Points)...
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