MATH 140 QUIZ 5 Name You must show your work for full credits. 1. Rewrite each summation using the sigma notation. Do not evaluate the sums. a) 3+4+5+...+93 +94 b) 1 . 21 + 2 . 22 + 3 . 23 + ... + 7 . 27 2. Describe the area between the graph of f(x)= sin(x), the x-axis, and the vertical lines at x = 0 and x = it as a limit of Riemann sums and as a definite integral. 3. Represent the limit of each Riemann sum as a definite integral. a) lim Ek=1 Ck AXk on [2,5] mesh+0 b) lim k=1(3 + Ck)AXk on [1,4] mesh -0 4. Using the area idea, determine the values of lim Ek=1(2ck)AXk on [1,3]. mesh+0 5. A robot has been programmed so that when it starts to move, its velocity after t seconds will be 3tz feet/second. a) How far will the robot travel during its first 4 seconds of movement? b) How far will the robot move between t = 1 second and t = 5 seconds? c) How many seconds before the robot is 343 feet from its starting place