W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable.If u(4, – 1) = - 4, us(4, – 1) = 2, uz(4, – 1) = 8, v(4, – 1) = 1, v,(4, – 1) = 5,ve(4, – 1) = - 3, Fu( – 4, 1) = - 9, and F.( – 4, 1) = 3, then find the following:%3D%3DW.(4, – 1) =W:(4, – 1) =

Introduction: A characteristic of severa actual variables, additionally referred to as a actual…

Answered: W(s, t) = F(u(s, t), v(s, t)), where F,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. u(3,-2) = -6 us(3,-2) = 4 u(3,-2) = -7 Fu(-6, -4) = 0 v(3,-2) = -4 Vs(3,-2) = 9 v(3,-2) = 1 F(-6, -4) = 7 Find We(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =
u = [-5, –1] v = [9, –7) w = [8, 1] 5u + v – w = | Ex: 6
1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b). 2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a), f(a+h, b), and f(a, b+ k) – f (a, b). %3D 3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h, and q = [f(x, y + k) – f(x, y)]/k. %3D SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES 411 4. Let f(x, y) = x² + 2xy + y². (a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b). (b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.
(a) f(2, 1, 2) (b) f(-3, 2, 1) (c) f(0, 0, 0) (e) f(t, 1², –t) (d) f(a, a, a) (f) f(a +b, a – b, b). 10. Let f(x, y, z) = zxy + x. Find (a) f(x+ y, x – y, x²) 11. Find F(f(x), g(y), h(z)) if F(x, y, z) = ye*yz, f (x) = x², 8(y) = y + 1, and h(z) = z². 12. Find g(u(x, y, z), v(x, y, z), w(x, y, z)) if 8(x, y, z) = z sin xy,u(x, y, z) = x²z°,v(x, y, z) and w(x, y, z) = xy/z. (b) f(xy, y/x, xz). %3D 2-3 %3D = TXyZ,
Suppose f(x, y) = (x2 – y² , 2xy, x*). Compute the following values: f(5, –6)= f(-6,5)= f(0,6)= f(f,5t)= f(s +t, s – t)=
Consider a function z = F(u(s, t), v(s, t)) where F, u, and u are differentiable and u(8, 6) = -1, v(8, 6) = 2, u, (8, 6) = 5, u, (8, 6) = 9, vs(8, 6) = −3, v₁(8, 6) = 4, Fu(-1,2) = -4, and F(-1,2)= -10. Compute and when s = 8 and t = 6 dt
Suppose f is a differentiable function of x and y, and g(r, s) = f(5r – s, s² - 6r). Use the table of values below to calculate g,(6, 3) and g,(6, 3). (27, -27) 4 8 1 (6, 3) 7 5 9 g,(6, 3) = g,(6, 3) = Additional Materials
Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. v(3,-2) = 0 Vs(3,-2) = 5 u(3,-2) = -3 Us(3,-2) = -7 ut(3,-2) = 7 Fu(-3,0) = -9 Vt(3,-2) = -1 Fv(-3,0) = -5 Find Wę(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =
Consider a function z = F(u(s, t), v(s, t)) where F, u, and v are differentiable and u(12, 8) = −12, v(12, 8) = −1, uş (12, 8) = −9, ut (12, 8) = −7, v§ (12, 8) = 9, vt (12, 8) = 1, Fµ(−12, −1) = −4, and F₂(-12, -1) = 8. əz дz Compute and when s = 12 and t = 8 Əs Ət

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W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable. If u(4, – 1) = - 4, u,(4, – 1) = 2, u:(4, – 1) = 8, v(4, – 1) = 1, v,(4, – 1) = 5, v:(4, – 1) = - 3, F.( – 4, 1) = – 9, and Fe( – 4, 1) = 3, then find the following: %3D | W.(4, – 1) = W:(4, – 1) =