af af əx' əy af and ду (1, -1) af Calculate when defined. (If an answer is undefined, enter UNDEFINED.) дх (1, -1) f(x, у) 4x2 - y° + x - 3 af ax af ду af ax |(1, –1) af ду |(1, -1) II II II

Q: The equations ry? + 3xzcos(u) + ye" = 6 and a*yz + xe" – 2u²v² = 6_are solved for u and v as…

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Q: If u = 2i - 3j + k and v = i + j - k, then u x v is:   (2, 5, 3) (2, 5, -3) (2, 3, 5) (2, -3, -5)…

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Q: Linear operator T: R2 R2 is defined by T(1,0) (1,4), T(1,1)-(2,2) T one-to-one?

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Q: z = f(st - 3, s2 +t) and fi(-1,9) = 3, f2(-1,9) = 7, fu(-1,9) = f12(-1,9) = f21(-1,9) = f2(-1,9) =…

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Q: The equations ry? + 8zzcos(u) + ye" = 16 and r*yz + xe" – 5u²v² = 15 are solved for u and v as…

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Q: letu= 43,5> Let V: L5,2> compute: a) proju u 5.) write u -w, +w,, where Wq is parallel to v and We…

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Q: Assume that 1<a<b and a/x+ x = 1 /(x - b) . Show that this equation is solvable.

A: Given that the equation, To solve the equation,

Q: 5. Let (ryz)" 1+y a) Compute the directional derivate of f(ay) at the point (1.1,-1) in the…

A: For a given vector f(x, y, z) the gradient vector denoted by ∇(f) is    ∂ /∂ x…

Q: 1) A (2, 5) and B (4, 3) V (x2 – x1) ^2 + (y2 – 1) ^2 V 2) F (1, 7) and G (6, 0) V (x2 – x1) ^2 +…

A: If we have given the coordinates of two points then we can easily find the distance between them…

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

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Q: 2z I 2 L (2,1, 2) dydadz I = -2/2 8 _z2 D I= f(x,y, z) dydxdz +2 2z-12 8 z2 22 2 • 2/2 8 z2 I = f(x,…

A: Given the triple integral

Q: Use the Wronskian and any needed theorems to show that f1 = sin x + 2x2 and f2 = e3x are linearly…

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Q: 3) Consider stress of a body at a particular point is give in the form of Q(x1, x2, X3) = xỉ – x –…

A: Given: Qx1,x2,x3=x12-x32-4x1x2+4x2x3   To find: An orthogonal change of variables that eliminates…

Q: Find af af and af 1. əx' əy' az f(x, у, z) 3D 18еХУZ af ax af %3D ay af az Find their values at (0,…

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Q: дz дz If z = x.f(xy), express x-y in its simplest form.

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Q: The Bernoulli's equation +y tanx = ysecx can be made linear upon multiplication by. and substitution…

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Q: U, +u, =0, 0<x<∞ 0<y<b ( u(0, y) = f(y), u(00, y) = 0 , , u(x,0) = 0 u(x,b) =0

A: Solving the partial differential equation by separation of variables.

Q: Let (w, x, y, z) = wxy + x² tan z and a = (1, -2,3,4). Then w(a): .₂(a) = -6 -2 8 60 -8 1-1 2 , (a)…

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Q: Let f(x,y,z) = x ^3+2yz-z^2 What is the steepest directional slope at the point (1,1,1)

A: Given function is  fx,y,z=x3+2yz-z2

Q: f(-1,3) = 4, fr (-1,3) = 5 and fy (-1,3), then the linear approximation to f(-1,3; 3,2) is

A: Formula: The linear approximation of function z=f(x, y) at point a, b is given by, z-fa,…

Q: Prove that Ix I - I y I ≤ I x - y I.

A: We have to prove that  x-y≤x-y We know, x+y≤x+y Then,  x=x-y+y⇒x=x-y+y≤x-y+y⇒x-y≤x-y

Q: O Fo = 0, F = 1, F, = F-2 F-1 %3D O F = 0, F2 = 1, F, = F2- F-1 %3D O Fo = 0, F = 1, F = F-2 + F-1…

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Q: 3. Using different colors draw secant lines from (1,2) to each of the points (x+Ax, F(x+Ax) ).

A: (1) graph the given equation  h(x)=x+12+2

Q: Let f(x,y,z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2,3)=-3 and fz(1,-2,3)=2. What is the…

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Q: Resolver los siguientes problemas de Cauchy pa primer orden: az az %3D a) y-x = 0 z(x,0) = x², ду az…

A: Given, y∂z∂x-x∂z∂y=o That is, yzx-xzy=0 The characteristic equations are dxy=dy-x=dz0 Taking first…

Q: Let f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2,3)=-3 and f,(1,-2,3)=2. What is the…

A: For directional derivative take dot product of gradf and unit vector of u

Q: Ques. 3: Check whether the operator T: R2 → R² defined by T(x,y) = (y,x) is linear. Moreover if T is…

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Q: 5. Let (ryz)" a) Compute the directional derivate of f(ay2) at the point (1.1,-1) in the direction…

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Q: c) Let f(x.y)= e. Find the directional derivative of f(xy) at the point (-3, 0) in the direction of…

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Q: (1 point) Let p(z) = 5x -8 and q(x) = VI-8. Find u(r) given that q(x) = p(u(x)). %3D %3D

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Q: 5. Let (ryz) 1+7 a) Compute the directional derivate of f(r.y) at the point (1.1,-1) in the…

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Q: azu Q5) Find u such that ax2 with u(x,0) = 0.5x2, u(x, 10) = 0, u(0, y) = 0, = 0 %3D u(20, y) = 1…

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Q: ow ow Ow For the functions w = xy + yz + xz, x=u+3v, y=u-3v, and zuv, express and using the chain…

A: This is a problem related to partial differentiation. Based on the chain rule we will provide the…

Q: Show mathematically that (10-6) is not independent of (10-1),(10-3), and (10-4).

A: We can write (10  -6) as:

Q: Write the given second order equation as its equivalent system of first order equations. u" + 4.5u'…

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Q: af Let f(x, y) = x³y + 8. Compute (1, 2) and -(1, 2). ax ду

A: Given: fx,y=x3y+8

Q: Let u and v be defined implicitly as functions of x and y by the equations xv + yu 5 x² – y3 + uv² =…

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Q: frxy, 2) =x*j+ x2 +xyZ direction of ū - (1,2,3) 10 5 in the

A: solution of the given problem is below...

Q: f(-1,–5)= f(-5,–1)= f(0, 0)= f(5, –5)= f(t, 2t)= f(uu, и — v)-

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Q: U₁ + Ux+Vx = 0, v₁ + UxVx = 0, u(x, 0) = u(x), v(x,0) = vo(x).

A: Given clear explanation below.

Q: Let f(x.y.z) be a function that satisfies fx(1,-2,3)=1, fy(1,-2.3)=-3 and f,(1,-2,3)=2. What is the…

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Q: A a,(x)y" +a-,(x)y"-|+...+a,(x)y'+a,(x)y=0 (x) y"-+ ...+a,(x)y'+a,(x)y=0 n-1 B a,(x)y" +…

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Q: {0, c, 5}. Let f (x) = x on [0, 5], and let P = Find two values of c in (0, 5) such that Uf (P) =…

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Q: u(0,t) = u(3,t)=0, t≥0 x 0<x<1 u(x,0) = 2-x 1<x<3

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Q: a) Let A = [-1, 1] = {x €R: -1<x< 1}. R = {(r, y) E A x A : ¤|+ |y| = 1 or |x| = |y|} %3D

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Q: The equations cy? + 6xzcos(u) + ye" = 12 and r³yz + ze" – 8u?u? = 24 are solved for u and v as…

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Q: ze ze dx' avikl-4,5), and f,(-4,5 For the functionz-f(x,y)%3D-5x+8y+3xy, find .3

A: *given:- z=f(x,y) = -5x3+8y2+3xy.