2) Draw a contour diagram for a function f(x, y) such that at the point (, y) (0,0),
23. The function f, whose graph and contour diagram are in Figures 12.89 and 12.90, is given by (x, y)(0,0), (x, y)(0,0 f (x, y) (a) Show that f(0, y) and f(x,0) are each continuous functions of one variable (b) Show that rays emanating from the origin are con- tained in contours of f. (c) Is f continuous at (0, 0)? xy/(a2 y2) Figure 12.89: Graph of z = en 35 -.35 15 157 -.15 .35 .35 Figure 12.90: Contour...
(1 point) A contour diagram for a function f(x,y) is shown below. 4 --- - -- --5 ---- - - 4 ----- Estimate the position and approximate value of the global maximum and global minimum on the region shown. Global maximum at Global minimum at
Multivariable Calculus Question 3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe 0.8 0.8 1.6 2.4 24 1.60.80.8 16 24 2.4 3. (2 pts) The contour diagram for a function, f(x, y) is shown below. Estimate the length of the gradient at point P. Be sure to show or explain your reasoning. 2.4 1.6 pe...
(1 point) Use the contour diagram for f(x, y) shown below to estimate the directional derivative off in the direction v at the point P. (a) At the point P = (2, 2) in the direction ✓ = 7, the directional derivative is approximately O‘ot 16.0 18.0 12.0 14.0 2.0 (b) At the point P = (3, 2) in the direction ✓ = -1, the directional derivative is approximately 8.0 (c) At the point P = (4,1) in the direction...
Select the contour map of the function. f(x,y) = y/(x^2+y^2)
2.1(9pts) Consider thc following contour plot for thc arbitrary function f(x,y): Y 0 2 Х -1 + 1. What is vf(0,0). Why? 2. At the point (0,2), in what direction should one move to increase the fastest? 3. Which vector has the greater magnitude: Vf(-1,0) or f(2,0)? CS Scanned with CamScanner
(1 point) Consider the function defined by ?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2 except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0. Then we have ∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)= ∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)= Note that the answers are different. The existence and continuity of all second partials in a region around a point guarantees the equality of the two mixed second derivatives at the point. In the above case, continuity fails at (0,0)(0,0). (1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2 < y s 2. Use a step size of 0.1. Add labels to the axis Problem 2: Create a surface plot and a contour plot of the function f(x, y) = xe-I(x-y2)*+y?] Where -2 x 2 and -2
x?sin’y If the function f(x y)= { x2 +2V2' (x,y) (0,0) is continuous at (0,0), then (x y) = (0,0) AK) Ox= 1/2 0-1 .k=0 ok=2 ok=1
A contour map for a function z=f(x, y) is given: Answer the following questions: Question 1. A contour map for a function z S(z,y) is given: -2 k-1 k-1- k-2 Answer the following questions. (a) (1 point) What is f(-1,1)? (b) (2 points) Describe the set of all points (r, y) such that f(z,y) = 0. Which of the following graphs best represents the graph of this function? (c) (1 point) B. A. D. Question 1. A contour map for...