A contour map for a function z=f(x, y) is given: Answer the following questions: Question 1....
[Question 1] Find and graph the domain of the function f(,y)-In-) Question 2] Graph a contour map of the function f(z, y)2s y 1 that contains four level curves. Make sure to find an equation for each level curve and label each one on the graph. IQuestion 3] The equation of the tangeat plane to the function z the equation: Using the form of the equatioa above, fiud the tangent plane to f(a,y)yat the point (2. ). Question 4] Find...
8.) (10 Points) Given the contour diagram z = f(x,y). 2 1 2 3 4 -2 R a. Find i. f(-1,1) 11. a value of x for which f(x, 1) = 3 iii. a value of y for which f(0,y) = -2 b. The given graph has a local maximum value. At which point (x,y) does this occur? c. Determine the sign (positive or negative) of the following partial derivatives. i. (1,0) ii. fy(0,1)
Consider the function below. y z= 2+x+ (a) Match the function with its graph (labeled A-F). (b) Match the function with its contour map (labeled 1-VI). O V VI Give reasons for your choices. Select- Also, the values of z approach 0 as we use This function is not periodic, ruling out the graphs in (b) Match the function with its contour map (labeled I-VI) II III IV V VI Give reasons for your choices. This function is not periodic,...
log(2 - 2) Consider the function f(x, y,z) (a) What is the maximal domain off? (Write your answer in set notation.) Find ▽f. (b) Find the tangent hyperplanes Ta2.1,f(r, y, 2) and To-ef(r, y, 2). Find the intersection (c) On (z, y, z)-axes, draw arrows representing the vector field F = Vf at the points (1,0,1), (d) Find the level set of f which has value ("height") wo 0, and describe it in words and of these two hyperplanes, and...
Select the contour map of the function. f(x,y) = y/(x^2+y^2)
make a contour map with x=0, y=0, z=0, z=1, z=2, and z=4 for z=x^2+y^2 then sketch graph
1. (a) Sketch a contour diagram for the function (x,y) y, and include gradient vectors at some various points. (b) Sketch a contour diagram for a function g(z,y), and include some gradient vectors, where the following propertics are satisfied The gradient vectors at points on the r-axis (other than the origin) are all parallel but never equal. In other words, for cach pair of distinct non-zero numbers ,2 there's some constant kメ1 such that ▽g(zi,0-k (Vg(T2,0). Vo(x,0)-Vg(r, 1) for all...
Answer the following questions for the given contour diagram of f(x, y) below: a. Estimate ∇f(4, 1) b. Estimate the maximum and minimum rates of change of f at the point (4, 1) c. In two different ways, estimate the rate of change of f at the point (4, 1) in the direction of the vector < −1, 1 > 17 1 아 IT 2p | 1b 1 1 19 2p | g + 이
17 marks] Consider the functionf(x, y) = (y - 1) (x- 1). (a) Find a unit normal vector to the contour line given by f=0.5 at the point (x,y) (1.5,2). Do not forget to check that this point is on the contour line. (b) Consider the curve L given by r(t) = 2ti+3tj with 0 ts1 and the Cartesian basis vectors i= (1,0) and j= (0,1) of R2. Determine using the chain rule and use this result to determine all...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...