True or False 15. If R is the disk {(x, y) 1r2+92 R, then JR f(x, y)dA 2T. 2) and f(x,y) 1 for every point (x, y) in 15. If R is the disk {(x, y) 1r2+92 R, then JR f(x, y)dA 2T. 2) and f(x,y) 1 f...
TRUE OR FALSE PRINGLE???? The point (-1,-1) is a saddle point for the function f(x, y) = x2 - y2 + 2(x - y). O True False Question 14 1 pts TRUE/FALSE: In order to optimize a differentiable function f(x, y)over the disk (filled in circle) x2 + y2 < 4, you first find all critical points in that disk, and then sort them by output. Then, you use the method of Lagrange Multipliers (perhaps) to optimize the function on...
(1 point) Let R be the rectangle with vertices (0,0). (8,0). (8, 8), and (0,8) and let f(x, y)- /0.25ry. (a) Find reasonable upper and lower bounds for JR f dA without subdividing R. upper bound lower bound (b) Estimate JRf dA three ways: by partitioning R into four subrectangles and evaluating f at its maximum and minimum values on each subrectangle, and then by considering the average of these (over and under) estimates overestimate: Inf dA underestimate: JRfdA average:...
Determine whether the statement is true or false. If false, explain why or give a counterexample that shows it is false. (2 pts each) b. If f(x,y) S g(x, y) for all (x, y) in , and both f and g are continuous over 2, then c. If f is continuous over 2 and 22, and if JJ, dA- jJa,dA, then f(x.y) dA- Jf(x.y) dA for any function fx,y). Determine whether the statement is true or false. If false, explain...
URGENT TRUE/FALSE 1 T F The intersection of 2 = 12 + y and rº + y² + 2 = 18 is a circle of radius 9. 2. T F = 2x + y is an equation of the tangent plane for f(z,y) = ry at the point where I = 1 and y=1. 3. T F Assume that (1,1) is a critical point for the function f(x,y) = 1 + y - 4ry+3. Then (1,1) is a local maximum...
1. Evaluate the iterated integrals: x2+2x+y a. JR 3x+3y dA, R: 15x32,0 sys 1 (Hint: Simplify the integrand first.) b. S ey/*dA where R is the region in the xy-plane bounded between y = x2 and y = x over the interval 1sx52. c. So Sex Sx**2 x dydzdx
true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If a unit vector u makes the angle of π/4 with the gradient ▽f(P), the directional derivative Duf(P) is equal to |Vf(P)I/2. F 12. There is a point on the hyperboloid 2 -y is parallel to the plane...
Question 14 1 pts TRUE/FALSE: In order to optimize a differentiable function f(x, y)over the disk (filled in circle) x2 + y2 < 4, you first find all critical points in that disk, and then sort them by output. Then, you use the method of Lagrange Multipliers (perhaps) to optimize the function on the boundary circle. Finally, you compare all special points and circle the biggest/smallest outputs and type them into webassign. True O False
1. True or false: (a) The constant term of the Fourier series representing f(x) 2,-2<2,f(x +4) f(z), is o 4 2 3 (b) The Fourier series (of period 2T) representing f(x)-3 - 7sin2(z) is a Fourier sine series (c) The Fourier series of f(x) = 3x2-4 cos22, -π < x < π, f(x + 2π) = f(x) is a cosine series (d) Every Fourier sine series converges to 0 at x = 0 (e) Every Fourier sine series has 0...
(5) Let f: [0, 1 R. We say that f is Hölder continuous of order a e (0,1) if \f(x) -- f(y)| . , y sup [0, 1] with 2 # 1£l\c° sup is finite. We define Co ((0, 1]) f: [0, 1] -R: f is Hölder continuous of order a}. = (a) For f,gE C ([0, 1]) define da(f,g) = ||f-9||c«. Prove that da is a well-defined metric Ca((0, 1) (b) Prove that (C ([0, 1]), da) is complete...
(2) The area of the surface with equation z = f(x,y). (x,y) E D. where fra f, are continuous, is A(S) = SVGC3. y)]? + [f;(x, y)]? +T dA If you attempt to use Formula 2 to find the area of the top half of the sphere x + y2 + 2? = a, you have a slight problem because the double integral is improper. In fact, the integrand has an infinite discontinuity at every point of the boundary circle...