(1 point) Suppose Vf2, y) = 5y sin(xy)i + 5x sin(xy)), F= f(x,y), and C is...
of 19 (0 complete) Evaluate the limit 5x² - 5y² lim xy)--(2-2) X+y Select the correct choice below and if necessary fill in the answer box to complete your choice 5x2 - 5y? ОА. lim xy--(2-2) x+y OB. The limit does not exist (Simplify your answer.) et points of R² is the following function continuous? 5 x, y) = x*(y² +81) ct the correct choice below and if necessary fill in the answer box to complete your choice 1. {(x,y)x+...
2. The force F(x, y) = (y + 2x) sin(xy + x)i + x sin(xy + x2) is conservative. (a) Find a potential V such that F = -VV. [2 marks] (b) Is F central? Provide a reason for your answer. [2 marks]
(1 point) Suppose F(x, y) = xyi + (x – y)j and C is the triangle from (4,0) to (-4,0) to (0,4) to (4,0). (a) Find the line integral of Ể along each segment of the triangle. Along C1, the line segment from (4,0) to (-4,0), the line integral is Along C2, the line segment from (-4,0) to (0,4), the line integral is Along C3, the line segment from (0,4) to (4,0), the line integral is (b) Find the circulation...
Previous Problem Problem List Next Problem f(x, y) (1 point) Consider the function f(x, y) = (e* - 5x) sin(y). Suppose S is the surface z (a) Find a vector which is perpendicular to the level curve of f through the point (5,4) in the direction in which f decreases most rapidly. vector -(eA5-5)sin(4)i+-(e^5-5(5)cos(4)j (b) Suppose above (5,4). What is a? 2i 8jak is a vector in 3-space which is tangent to the surface S at the point P lying...
Consider F and C below. F(x, y, z) = yz i + xz j + (xy + 10z) k C is the line segment from (3, 0, -3) to (4, 4, 1) (a) Find a function f such that F = Vf. f(x, y, z) = (b) Use part (a) to evaluate [s vf. dr along the given curve C.
Q6 [10+1+3=14 Marks] Let F be a force field given by F(x, y) = y2 sin(xy?) i + 2xy sin(xy?)j. (a) Show that F. dr is exact by finding a potential function f. (b) Is I = S, y2 sin(xy2) dx + 2xy sin(xy?) dy independent of path C? Justify your answer. (c) Use I to find the work done by the force field F that moves a body along any curve from (0,0) to (5,1).
Find the derivative of the function. y sin-1(5x+ 1) Part 1 of 3 The function y - sin-1(5x + 1) is a composition, and so we must use the Chain Rule, given below, to find the derivative dx[f(g(x))) = f '(g(x))g'(x) For the given function sin 1(5x+ 1), the "inside" function is Sx + and the foutside" function is arcsin (a) Part 2 of 3 Recall that the derivative of y sin-1(x) is 1-(5x - 1)2
Find the derivative of...
Suppose f(x,y)=xy(1−10x−4y)f(x,y)=xy(1−10x−4y). f(x,y)f(x,y) has 4 critical points. List them in increasing lexographic order. By that we mean that (x, y) comes before (z, w) if x<zx<z or if x=zx=z and y<wy<w. Also, determine whether the critical point a local maximum, a local minimim, or a saddle point. First point (____________,__________) Classification: Second point(__________,__________) Classification: Third point (___________,_________) Classification: Fourth point (__________,_________) Classification:
1.) Let f(x, y, z) = xy?z3 – sin(xy) +erz? – tan(y, 3. Determine the following. (a) e (b) (c) azonos
Let f(x, y) = 5x2 - 4x + 5y + 4y2 + 8xy List the critical point: Preview The critical point is a Select an answer Get help: Video