Find the Taylor polynomial P3(x, y) of degree three of the function f(x, y) = sin(xe") at the point (0, 0). P3(x, y) =

Q: Find y as a function of a if y(0) = 7, y/(0) = -12, y'(0) = 108. y(x) = y" + 36y' = 0,

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Q: 1 x, and the line perpendicular to 6 Find the area of a triangle bounded by the y axis, the line f…

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Q: Express f(z) = x-1-iy (x−1)² + y² in terms of z.

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Q: Find the number of zeros of f(z) = z' + iz² – z + 2i in the upper half-plane.

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Q: -2+z) ds over t e point (0, 0, 0)

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Q: Calculate fx (1, 3) and fy (1, 3) for f (x, y) = √(7x + y^2).

A: For a function of two variables, partial derivative with respect to one variable is calculated by…

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) × r"(t). P(C) = 21²1 - 48 + ²P²H 2³k r(t) 3 (a) r(t) 3it…

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Differentiate the function. r(t) = (3²- + 8)i + r'(t) = (6t)i + ( 132 r'(t) = i + (6t)j r'(t) =…

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Q: Let f(x, y) = 3x² + 4y? – axy. (a) Find the values of a such that the graph of f increases when…

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Q: ху lim (x,y)→(0,0) Vx²2+y2 Get the value of

A: This is the problem based on multivariate calculus. To find the limit , we can convert given…

Q: Find the gradient of cos(xy) – 3y4 + 3 at the point (1,4) -

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Q: Let q = - 2xy - y² + 2xz+2yz + z² be a quadratic form on R³ viewed as a polynomial in 3 variables.…

A: To find the canonical form of the quadratic form using Sylvester's law of inertia, we need to…

Q: Find all residues of the function z (2-2) not including the residue at infinity. "

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Find y as a function of a if y(0) = 8, y(0) = 4, y"(0) = 134. y(x) = y"8y" -y + 8y = 0,

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Q: Find the image of the line z =3 +iy under f(z) = e

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Q: 8. Consider the complex function f(z) = x² + y² + 2ixy. a) Show that f'(31) does not exist. b) Show…

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Q: Determine R³(t) if R²' (t) = <2e²+-41, +/= 1+1) and R (2) = <3, -5,0).

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