4. (a) Verify the divergence theorem in the plane for Fryi+ (2x - y)j and C is the triangle with vertices at (0,0), (1,0) and (0, 1). (b) Find the circulation of F around the curve C above. (c) If (velocity), give physical interpretations of funds and § ¨· dÄ. =
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- Let vector r(t) = <5sin(t), 5cos(t), 2t^(3/2)> be the position function of an object.a. Find vector v(t) and vector a(t), the velocity and acceleration of the object.b. Find the speed of the object.c. Find the distance the object travels on the interval [0, 1]. Also find the average speed of theobject on this interval.B A' A is the point (3, 1). Bis the point (a, 11). The gradient of AB is 5/2 -1 2 O 7show full and complete procedure HANDWRITTEN only
- Write down the parametric and nonparametric equations of the tangent plane to the graph of function f(x,y)=xy+y2 at the point(3,2), f(3,2)).Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x2 −0.01y2 where x, y,and z are measured in meters, and you are standing at a point with coordinates (60, 40, 966). The positivex−axis points east and the positive y−axis points north. Find a vector representing the direction of largest slope at point P. What is the rate ofascent in that direction?Find a vector representing the direction where there is zero slope at the point P .Suppose that the directional derivative of a function f at a point Pin the direction of the vector ū = (-1,0) is - Relate this 4 value to the behaviour of f. A. From the point P, the function f is increasing at a rate of - in the positive x-direction. B. From the point P, the function f is increasing at a rate of - in the positive y-direction. C. From the point P, the function f is decreasing at a rate of - in the negative y-direction.
- Let u(t) = 2t'i+ (P -7)j-8k and v(t) = e'i+3 ej- ek. Compute the derivative of the following function. 3t L u(t) • v(t) Select the correct choice below and fill in the answer box(es) to complete your choice. O A. The derivative is the scalar function 訓 這 O B. The derivative is the vector-valued function (i+ (Dj+ ( k.Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x² 5ху + хуz (a) Find the rate of change of the potential at P(5, 4, 7) in the direction of the vector v = i +j - k. (b) In which direction does change most rapidly at P? (c) What is the maximum rate of change at P? Need Help? Watch It Additional Materials lеВookJust question d),please