УЛ [10 pts] The figure to the right shows the level curve of f(x, y) =...
Question 7 (8 points) Let vf(x,y) denote the gradient field for the function f(x, y) = x2 - y. Sketch a level curve and two gradient field vectors on the level curve.
4. (8 pts.) The level curves of z = = f (x, y) are given along with the constraint curve g(x, y)= 8 9(x, y) = 8 40 50 60 70 0 30 20 10 a. Maximize and minimize f on the constraint. b. Label the point where the maximum occurs as A and the point where the minimum occurs as B. c. Sketch in the approximate vectors Vf and Vg at the points A and B.
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
2. (4 pts.) Which of the following are the level curve graphs for f(x,y)=et-y ? : Which of the following are level curves for the function f(x,y)=2*-? (A) (B) (C) (D) (E) (G) (H)
Section 15.1 Worksheet Find the gradient field F = νφ for the potential function φ. Sketch a few level curves of φ and a few vectors of F. φ(x, y)-yx2+ y2 for x2 + y2 2. 9, (x, y) # (0,0) Section 15.1 Worksheet Find the gradient field F = νφ for the potential function φ. Sketch a few level curves of φ and a few vectors of F. φ(x, y)-yx2+ y2 for x2 + y2 2. 9, (x, y)...
f 2. Figure 10 shows a constraint 9 (x, y) = 0 and the level curves of a function f. In each case, determine whether has a local minimum, a local maximum, or neither at the labeled point. 4 3 2 Vf Vf 4 3 2 А B g(x, y) = 0 g(x, y) = 0 Rogawski et al., Multivariable Calculus, 4e, © 2019 W. H. Freeman and Company FIGURE 10
3. The diagram shows a part of the curve y=f(x). (a) For what values of x is f '(x) = 0? (b) For what range of values of x is f'(x) <0?
the figure shows a vector force field F(x,y) mapped in the x-y plane. (It depicts a vector quantity whose magnitude and direction varies only with x and y, Not z). Several points (A, B, and C) are indicated, and a (dashed) path from A to B is shown. F(x, y) =
9. The work done by the force F(x, y) (2at +e) i (4y in moving a particle -re from (0,0) to (1,1) along the curve y =x4 needs to be calculated. a. Show that F is a conservative vector field. b. Describe three different ways to calculate the work. Answer: 3 +1/e c. Calculate the work by a method of your choice.. a. Show that F=(y+yz) i + (x + 32 + xz) j +(9yz2 + y 1) k is...
Question 6 14 pts Consider the curve C defined by the parametric equations: x f(t) y= g(t) = sint -t costt (d) Which picture shows the curve C? Recall the curve C is defined by : x= f(t) cos t g(t) = sint - t y 20 20 10 10F 0 -10 -10 -20 -20 -20 10 -20 10 C 20 -10 0 10 (i) (ii) X 20 20 10 10 0 0 10 -10 -20 -20h -20 10 -20...