Suppose C is the boundary of region R = {( x , y ): x 2 ≤ y ≤ 1},oriented counter clockwise (see figure); F = 〈 1 , x 〉 . a. Compute the two-dimensional curl of F and determine whether F is irrotational. b. Find parameterizations r 1 ( t ) and r 2 ( t ) for C 1 and C 2, respectively. c. Evaluate both e line integral and the double integral in the circulation form of Green’s Theorem and check for consistency. d. Compute the two-dimensional divergence of F and use the flux form of Green’s Theorem to explain why the outward flux is 0.
Suppose C is the boundary of region R = {( x , y ): x 2 ≤ y ≤ 1},oriented counter clockwise (see figure); F = 〈 1 , x 〉 . a. Compute the two-dimensional curl of F and determine whether F is irrotational. b. Find parameterizations r 1 ( t ) and r 2 ( t ) for C 1 and C 2, respectively. c. Evaluate both e line integral and the double integral in the circulation form of Green’s Theorem and check for consistency. d. Compute the two-dimensional divergence of F and use the flux form of Green’s Theorem to explain why the outward flux is 0.
Suppose C is the boundary of region R = {(x, y):x2 ≤ y ≤ 1},oriented counter clockwise (see figure); F =
〈
1
,
x
〉
.
a. Compute the two-dimensional curl of F and determine whether F is irrotational.
b. Find parameterizations r1(t) and r2(t) for C1 and C2, respectively.
c. Evaluate both e line integral and the double integral in the circulation form of Green’s Theorem and check for consistency.
d. Compute the two-dimensional divergence of F and use the flux form of Green’s Theorem to explain why the outward flux is 0.
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Use undetermined coefficients to find the particular solution to
y"-2y-4y=3t+6
Yp(t) =
Car A starts from rest at t = 0 and travels along a straight road with a constant acceleration of 6 ft/s^2 until it reaches a speed of 60ft/s. Afterwards it maintains the speed. Also, when t = 0, car B located 6000 ft down the road is traveling towards A at a constant speed of 80 ft/s. Determine the distance traveled by Car A when they pass each other.Write the solution using pen and draw the graph if needed.
The velocity of a particle moves along the x-axis and is given by the equation ds/dt = 40 - 3t^2 m/s. Calculate the acceleration at time t=2 s and t=4 s. Calculate also the total displacement at the given interval. Assume at t=0 s=5m.Write the solution using pen and draw the graph if needed.
Chapter 17 Solutions
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University Calculus: Early Transcendentals (4th Edition)
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