advertisement

MATH 101 SAMPLE MIDTERM 1 For full credit, please show all work. Time: 50 minutes. Books, notes, calculators, or other aids are not allowed. √ 1. (6 marks) Write the upper and lower Riemann sum for the function f (x) = x on the interval [1, 3] corresponding to the partition of [1, 3] into n intervals of equal length. (Do not evaluate the sums!) 2. (6 marks) Let ( f (x) = 4x − 3, 0 ≤ x ≤ 2 9 − x2 , 2 ≤ x ≤ 3. Find the average value of f on the interval [0, 3]. 3. (12 marks) Evaluate the following integrals: Z 2 dx (a) , 2 1 x(1 + ln x) Z (b) cos(2x) cos x dx. 4. (8 marks) Find the area of the finite plane region bounded by the curve y = xex and the line y = ex. Z 2x−x2 5. (8 marks) Let F (x) = √ 2 + sin( 100 − t) dt for 0 ≤ x ≤ 4. Find the x where F 0 attains its maximum value on the interval [0, 4]. 1