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Practice Questions

# Practice Questions - MIT OpenCourseWare http/ocw.mit.edu...

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MIT OpenCourseWare http://ocw.mit.edu 18.01 Single Variable Calculus For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Fall 200 6

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18.01 Practice Questions for Exam 3 Fall 2006 1 �/ 2 x dx 3 1. Evaluate a ) b ) cos x sin 2 x dx 2 0 1 + 3 x �/ 3 1 2. Evaluate x dx directly from its definition as the limit of a sum. 0 n 1 Use upper sums (circumscribed rectangles). You can use the formula i = n ( n + 1). 2 1 3. A bank gives interest at the rate r , compounded continuously, so that an amount A 0 deposited grows after t years to an amount A ( t ) = A 0 e rt . You make a daily deposit at the constant annual rate k ; in other words, over the time period t you deposit k t dollars. Set up a definite integral (give reasoning) which tells how much is in your account at the end of one year. (Do not evaluate the integral.) 4. Consider the function defined by F ( x ) = x 3 + sin t dt . Without attempting to find 0 an explicit formula for F ( x ), a) (5) show that F (1) 2; b) (5) determine whether
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