MATH 140 Midterm: MATH140 JOHNSON-G FALL2007 0101 MID EXAM 4

• School: University of Maryland
• Department: Mathematics
• Course: MATH 140
• Professor: All

Document Summary

Your solutions should read nicely and be legible. They should not be composed of regurgitated fragments of your mind scattered about the page. 1. (a) let f (x) = sin(x) and let p be the partition of the interval [0, 2 ] de ned by p = Compute lf (p ). (b) let h(x) be any continuous function that satis es 4 h(x) x2 4 for 0 x 1. x3h(x) dx. Find upper and lower bounds for z 1. [15 pts: find the area of the bounded region between the graphs f (x) = x3 and g(x) = x. 3. (a) use logarithmic di erentiation to nd f (x) when f (x) = x3/2e (x2) 1 ex (b) evaluate d dx z sin(x) x2 ln|t| dt: evaluate the following: (a) z x2 x 1 dx (b) z 2. [10 pts: find the average height of a castle door bounded by the parabola y = 4 x2 and the x-axis.