Consider f(x,y)= = y sin(y e3*). Then which one of the following is correct Ol fux,...
السؤال 4 of f(x, ) = in(ex cos(m), then which of the following combination is correct fxxx,y)=0 O fyx.) - - x cos(y) fxx.y) = sin(y) fxlx.y) - fylx.y) - sin(y) fxlx.y) -- cos(y) fxx(x,y)=0 fylx.) = -x cos(y) fxlx,y) = -x sin(y) fxxx.v) = 0 O fwlx.v) - - x cos(y) f»{x,y) = cos(y)
Prove the trigonometric identity: sin(x + y) sin(x - y) = sin’x – sin? y. Which identity is used to prove it true? sin(x + y) = sin x cos y - cos x sin y All of these. tan o sin e cos e cos? 0 = 1 - sin? 0
= Consider the vector field F(x, y) (cos y + y cos x)i + (sin x – xsin y)j. Show whether the function f(x,y) = x COS Y – y sin x is a potential function for the vector field, F.
Consider the vector field. F(x, y, z) = (3ex sin(y), 3ey sin(z), 5e7 sin(x)) (a) Find the curl of the vector field. curl F = (-3d"cos(z))i – (36*cos(x)); – (5e+cos(y) )* * (b) Find the divergence of the vector field. div F = 3e'sin(y) + 3e'sin(z) + 5e+ sin(x)
3. (7 points) Consider the function sin f (x, y) = { if (x, y) + (0,0) if (x, y) = (0,0) (a) Prove that f is differentiable at (0,0). (b) Prove that f is not C1 at (0,0). (Hint for part (a): Begin by showing that fx(0,0) and fy(0,0) exist and find their val- ues, and thereby determine Jf(0,0).)
x (0,0)=(3+4 sin cos e, +(3+4 sin º) sin 0 e2+ 4 cos 0 e3 The value of Jxoxxo/ at 9 = 1 is: 21 28 O 49
Which one is the solution to this equation (1 + y2 sin 2x)dx – 2y(cos x){dy = 0 denkleminin çözümü aşağıdakilerden hangisidir? 19- x + √y²+1=c O A) xy - Inx=0 B) x-y(cos x)2 = C xye-y - 2 = 0 D) ce-x = y E
7. Show that the following functions u(x, y) monic functions v(x, y) and determine f(z) = u(x,y) + iv(x, y) are harmonic, find their conjugate har- as functions of 2. 2x2 2лу — 5х — 22. Зл? — 8ху — Зу? + 2у, (а) и(х, у) (b) и(х, у) (с) и(х, у) (d) u(a, y) 2e cos y 3e" sin y, = 3e-* cos y + 5e-" sin y, = elx cos y - e y sin y, (e) u(x,...
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...
(2) Consider the function f(x,y) = cos y + sin y (a) Compute the local linearization of f(x,y) at (0,5). (b) Compute the quadratic polynomial for f(x,y) at (0,). (c) Compare the values of the linear and quadratic approximations in part (a) and (b) with the true values for f(,y) at the points (0.007,), (0,0.7924) and (0.7 ). Which approximation gives the closest values ?