Let f be a differentiable function of one variable, and let w = f(p), where p (x2 +y2 + z)/2, Show that me, me, (dw ax ay az dp

Q: Let f = zy + yx, v = [y, z, 4z - x], w Find - [vª, zª, x®]. (a) grad f and f grad f at (3, 4, 0) (b)…

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Q: (a) Find the points (x ,y, z) in space, where the function f(x, y, z) = Vx² +y -1 Is continuous.

A: It is well known that the equation z=x2+y2 represents a circle with centre at the origin. The…

Q: xy Prove that the function f(x, y) is differentiable everywhere in its do- x² + y? main.

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Q: Show that the function u e(xy) + Vry V(y/x) provides the quation = 0. dy?

A: Again differentiate,

Q: Let f(x,y, z) = xtan (Vyz)- sin(e*) , evaluate zy %3D дудхда

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Q: f(z) is a twice differentiable function with f(0) = 1, f(2) = 4, f'(2) = 5, Then af"(x)dx = %3D

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Answer of the above differential equation is

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)\/2.…

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Q: Let f (z)be an analytic function, which is represented by f (z) = u (x, y) + iv (x, y) where z = x+…

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Q: Let f be a differentiable function of one variable, and let f(p), where p = (x² + y² + z²)'/2. Show…

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Q: Show that if r(t) = ƒ(t)i + g(t)j + h(t)k is differentiable at t = t0, then it is continuous at t0…

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Q: sume that f(t) is continuous on [a, b| and that u = g(t) is cont ferentiable on [a, b], then f(u)…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show…

A: Given: w=fx,y, x=rcosθ, y=rsinθ If w is a multi variable function w(x,y,a,........z) thus the…

Q: Prove that the function f : R? → R, f(x, y) = sin(/x² +|sin y|) is uniformly continuous on R?.

A: The time interval between two waves is known as a Period whereas a function that repeats its values…

Q: If f(r) is a differentiable function of r = |F] then show that f(r)i is irrotational. Find f(r) so…

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Q: 4. If f is a differentiable function of a and y with w f(x, y), x =r cos 0 and y = r sin 0, %3D show…

A: To verify the given relations between partial derivatives.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given:     x2 + y2 = 100

Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: At what points (x,y,z) in space are the functions continuous? a. h(x,y.z) = In (3z° - 4x- 5y- 4) 1…

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Q: Let f be a differentiable function of one variable, and let w = f(p), where p = (x² + y² + z?)!/2.…

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Q: Consider the function f : ACR? → R given by: {* zty 4y² > 0, (x, y) ± (0,0), f(r, y) = (x, y) =…

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Q: Let z = t*f (x, y) with f be a differentiable function. If x = t2 + u2 and y = t*u3, then ∂z/∂t…

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Q: c) Let f(r, y) = Vlry| Prove that f(r, y) is not differentiable at point (0, 0).

A: Given a function : f(x,y)=xy We need to show that f(x ,y) is not differentiable at (0 ,0). Let's…

Q: Show that f is continuous at (0, 7) where a cos y + y(e" – 1) if r + 0 f(x, y) = ay if æ = 0.

A: In the given question we have to show that the given function f(x,y) is continuous at the point…

Q: If f(x,y)is integrable function on the rectangle R = [a, b] x [c,d] where (a, b] on the x- axis and…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Suppose that F(x,y, z) = 0 defines z as a function of x and y and F is differentiable. Prove that дх…

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Q: Let u be a differentiable function of x. Use the fact that ∣u∣ = √u2 to prove that

A: Given that - u = u2          ............(1)To prove - ddxu = u'uuProof - Difefrentiating equation…

Q: (a) Let Ty if +y +0, g(x, y) = 0 if r = y = 0. Prove that g(r, y) is continuous at (0,0).

A: To Prove: g(x,y) is continuous at (0,0)

Q: Suppose z = f(x, y) is a differentiable function of x and y, x =r cos 0, and y =r sin 0. (a) Compute…

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Q: Show that the function u = p(xy) + VrY v(y/x) provides the uation x2 = 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Suppose that z = f(x, y) is differentiable at the point (1024, 1024) with f,(1024, 1024) = 5 andf,…

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Q: Let v^5n+u^2n v^3n=n^2+ve^(u^2n ) define v as differentiable function of u, find dv/du at (0,-n),…

A: To solve the following problem

Q: (a) If A = (4xy – 3x²2²)i + 2x?j – 2x°z k, prove that A dr is independent of the curve C joining two…

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Q: Show that the function u = p(xy) + Vry v(y/x) provides the quation = 0. dy?

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Q: Suppose r lIs a differentiable function of x and y, and g(u, V) = (e sin(V), V)). Use the table of…

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Q: Suppose that z = f(x, y) is differentiable at the point (27, 81) withf,(27, 81) = 2 and f, (27, 81)…

A: Given that:                            z=f(x, y)fx(27, 81)=2fy(27, 81)=-6x=t3y=t4

Q: Suppose that z = x + iy ∈ C and consider the function f(z) = y^2  + ix^2 Determine where f(z) is…

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Q: Let f(r, y) 3ry? when (x, y) + (0,0) and f(0,0) = 0. g²+2y! At which points is f continuous?

A: The given function is: This function is continuous at a point if at that point limit exists and the…

Q: 44. Let f(x, y) = g(u), where u = x² + y² and g(u) is differentiable. Prove that 2 4u (dg Әх du

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Q: Suppose that z = f(x, y) is differentiable at the point (64, 1024) withf, (64, 1024) = 3 and dz…

A: Topic:- partial derivative

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Let f be an arbitrary differentiable function of x, y and z, and let x = 2u-v. y =v-2w and z = w-2u.…

A: Given: f is arbitrary differentiable function of x, y, z and x=2u-v, y=v-2w and z=w-2u. To find: The…

Q: Suppose that z=f(x,y) is a differentiable function of x and y with (1,2)= 4, ze (1,2)=2. If x=x(t)…

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Q: Suppose that f:I → R and g: I → R are differentiable at c E I. Then, a) If k E R, then the function…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: (a) Differentiate the functions w.r.t t, ddtx2+y2=100 2xdxdt+2ydydt=0 Substitute the given values,