a. Show that the maximum value of a2b2c2 on a sphere of radius r centered at...
Question 8
(a) Determine, without graphing, whether the function has a minimum value or a maximum value (b) Find the minimum or maximum value and determine where it occurs. (c) Identify the function's domain and its range. f(x) = 3x² - 244-7 (a) The function has a value. (b) This value is . It occurs at x = | (c) What is the domain off? O A. (XIX is all positive numbers) OC. (XX4) OB. (XIX > 4) OD. (XIX...
Given the function 1 f(x,y) = answer the following questions. 36 - 16x2 - 16y2 a. Find the function's domain. b. Find the function's range. c. Describe the function's level curves. d. Find the boundary of the function's domain. e. Determine if the domain is an open region, a closed region, both, or neither. f. Decide if the domain is bounded or unbounded. a. Choose the correct domain. OA. 9 The set of all points in the xy-plane that satisfy...
6. Estimates from geometric definitiions: (a) Suppose divF2z. Estimate the ux of F through a sphere of radius 0.01 centered at (b) Suppose curlF-(z + 4)it (2-ทั+ (:-3)E, estimate circulation of F around a circle C of radius 0.1, centered at the origin, if C is on the ry- yz-, and rz-plane respectively oriented counter-clockwise when viewed from the positive z, positive a, and positive y-axis respectively 7. Three small squares Ci,C2, Cs each with sides 0.1, centered at the...
For the given function, complete parts (a) through (f) below. f(x,y) = -(22+272) (a) Find the function's domain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The domain is all points (x,y) satisfying (Simplify your answer. Type an inequality.) OB. The domain is the entire xy-plane (b) Find the function's range. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O...
Problem 81 Find the point farthest from (1,3,-1) such that x2 + y2 + z2-11 and x-y+z < 3. What happens to the maximum distance if the 11 on the right side of the inequality is perturbed? 81. Suggestions (a) Take as objective the square of the distance from (x, y, z) to the point given (b) For the case of points inside the given sphere and with x-y+ z = 3, you might solve the Lagrange equations for x,...
Give parametric equations that describe a full circle of radius
R, centered at the origin with clockwise orientation, where the
parameter t varies over the interval [0,22]. Assume that the
circle starts at the point (R,0) along the x-axis.
Consider the following parametric equations, x=−t+7, y=−3t−3;
minus−5less than or equals≤tless than or equals≤5. Complete parts
(a) through (d) below.
Consider the following parametric equation.
a.Eliminate the parameter to obtain an equation in x and y.
b.Describe the curve and indicate...
Test: Final Exam Review 34 of 44 (0 complete) This Question: 1 pt Find the potential function f for the field F. F=2xe +yi+2ye+yj ex2.y2 O A. f(xy,z)2 +C O B. fxyz) 2ey +C OC. fixy.z)ete +C O D. fixyz)= ey+C Test: Final Exam Review This Question: 1 pt 35 of 44 (0 complete) Using Green's Theorem, compute the counterclockwise circulation of F around the closed curve C. F=xyi+xj.C is the triangle with vertices at (0,0), (2,0), and (0,2) OA....
The base of the closed cubelike surface shown here is the unit square in the xy-plane. The four sides lie in the planes x=0, x= 1, y = 0, and y= 1. The top is an arbitrary smooth surface whose identity is unknown. Let F= xi – 2yj + (z + 3)k and suppose the outward flux of F through Side A is 1 and through Side B is - 3. Can you conclude anything about the outward flux through...
First, verify that y(x) satisfies the given differential equation. Then, determine a value of the constant C so that y(x) satisfies the given initial condition. Use a computer or graphing calculator to sketch several typical solutions of the given differential equation, and highlight the one that satisfies the given initial condition. y' =y+3; y(x) = CeX-3; y(0) = 8 What step should you take to verify that the function is a solution to the given differential equation? O A. Differentiate...
please answer all qustion on expination needed
1 Find a vector of magnitude 3 in the direction of v=5 i - 12 k The vector is i+i+k (Simplify your answer. Use integers or fractions for any numbers in the expression) 2 Give a geometric description of the set of points in space whose coordinates satisfy the given pairs of equations x2 + y2 +(2+152 = 169, z= - 3 Choose the correct description O A. The line through (5,0. -...