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(1 point) Suppose the average value of f(x) on the interval (5,9) is 65. Calculate s...
1. A car travels 30 miles north, then 10 miles east. The displacement vector is X miles north, Y miles east. A) What is X? B) What is Y? 2. A car travels 30 miles north, then 10 miles east, then 20 miles west, then 2 miles south. The displacement vector is X miles north, Y miles east. A) What is X? B) What is Y? (beware of signs) 3. A car travels 30 miles northwest. The displacement vector is...
PROBLEMS and QUESTIONS 1. An object moves across the floor and comes to a stop. Explain how Aristotle and Galileo would view this motion differently. 2. Explain the difference between speed and velocity and give examples of each. 3. Explain how an object can have a constant speed and a varying velocity. 4. What are the units of acceleration? 5. If an automobile travels at the rate of 40 miles per hour, how long will it take to travel 400...
11. The graph of fis shown. Determine the value of f (x)dx= y = f(x) - X 16 32 48 64 1 12. Consider the definite integral s sin(tw) dw. What is the interval of integration for this integral? What is the variable of integration? What is the integrand? 13. Suppose that f* f(x) dx = 5, ſ. f(x)dx = -3, * g(x)dx = -1 and 1 g(x)dx = 7. Determine the value of each integral. Box Answer (5) $(x)+...
(1 point) Find the average value of : f(x) = 6/ on the interval [1, 36). Average value =
point) Your task is to estimate how far an object traveled during the time interval 0 S t S 8, but you only have the following data about the velocity of the object. time (sec) 01 2 3 4 5678 velocity feet/sec)-24-3-4-2-3231 get an idea of what the velocity function might look like, you pick up a black pen, plot the data points, and connect them by curves. Your sketch looks something e the black curve in the graph below....
9. Find the average value of f(x) = 3x2 - 2x on the interval [1,4]. (8 Points) Hint: Use the formula: favo = 6-a Srca) dx
(1 point) What is the average value of f(x) = x2 over the interval [5,6]?
11. (4pts) Find the average value of the function f(x) = 4.1 over the interval [3,5]. 12. (4 points) Let Pn := {20,21, ..., 2n} a partition of the interval [3,5); 20 = 3, 2n = 5, by || P1 || we denote the norm of the partition. Define Alk = xx – Ik-1 and cx = 3.2k-1 + 2 tk. What integral equals the following limit n lim || P1102 k=1 Ĉ(2) Alk C +
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle from (4,0) to (-4,0) to (0,4) to (4,0). (a) Find the line integral of Ể along each segment of the triangle. Along C1, the line segment from (4,0) to (-4,0), the line integral is Along C2, the line segment from (-4,0) to (0,4), the line integral is Along C3, the line segment from (0,4) to (4,0), the line integral is (b) Find the circulation...
(1 point) Consider the function f(x) = on the interval [4,9]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a c in the open interval (4,9) such that f'(c) is equal to this mean slope. For this problem, there is only one c that works. Find it.