5.1 Homework - Area and Distance Problems (Homework)

1. [-/1 Points] DETAILS SCALCET9 5.1.009.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance (in ft) that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 5.7 1 1.2 15.5 18.8 19.4 20.2 lower ft upper ft Need Help? Read It Watch It Master It 2. [-/1 Points] DETAILS SCALCET9 5.1.014. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER The graph of the velocity of a car accelerating from rest to a speed of 75 km/h over a period of 30 seconds is shown. v (km/h) 75 50 25 0 10 20 30 t (seconds) Use this graph and a midpoint Riemann sum with six equal subintervals to estimate the distance traveled (in km) by the car during this time period. (Round your answer to two decimal places.) km Need Help? Read It3. [-/1 Points] DETAILS SCALCET9 5.1.016. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Use this definition with right endpoints to find an expression for the area under the graph of f as a limit. Do not evaluate the limit. f ( x ) = xe*, osx$5 A = lim n - 00 Need Help? Read It 4. [-/1 Points] DETAILS SCALCET9 5.1.022. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Determine a region whose area is equal to the given limit. Do not evaluate the limit. lim 2 1+ 21 1 -+ 00 O v 1 + x on [0, 2] Ovi + x on [-2, 2] O 2v 1 - x on [0, 2] O 2\\ 1 + x on [0, 2] O 2v 1 + x on [-2, 2] Need Help? Read It5. [-/1 Points] DETAILS SCALCET8 5.1.JIT.009.MI.SA. MY NOTES ASK YOUR TEACHER This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise Find the sum of the infinite series. Step 1 Consider the infinite sequence a 1, a2, a31 . ap ... The sum of all the terms of the infinite sequence is called an infinite series and is denoted by a, + azy ,ta, + ... +a+ ... = a , Expand the given series. 3 3 3 3 10 102 104 105 = 0.3 + 0.03 + + 0.0003 + 0.00003 + ... Submit Skip (you cannot come back)