) The domain of the function y = In(1 – x²) is R – [-1,1].

Q: Let f(x, y) = - 4xy² – 2x² + 8y². Find and classify the critical points of f.

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: 25-let F(xs.2)=x-x22 @ Find VF 6 write the equution of tngent Plame to the at Paint (2,1,1). Find…

A: The given function is,  F(x,y,z)=x2y2-xz2 We have to find,  a) ∇F b) Equation of the tangent plane…

Q: 1. Find where f(x, y) = 4x² + 8y? – 4x – 8y +5 has absolute extreme values over the square with…

A: To calculate the extreme values of f(x,y)bounded by the square, the following calculations need to…

Q: 18.7. Let f(z) = (e + e-2)/2. Evaluate f(2) -dz, where y is any %3D simple closed curve enclosing 0.

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Q: hich z ∈ C the function e^(1/z) is holomorphic?

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Q: 3) Evaluate f (xy + 2z)ds. C is the line segment from (1,0,0) to (0,1,1).

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Q: 2. Let f(x, y) = In(x² + y²). Show that fre + fyy = 0. %3D

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Q: Q2: Expand f(x,y) = [sin (x y³)]² about (5, 1).

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Q: Q1: If Z = f(x·y) + g. Prove that x² - Zxx + x· Zx = y² · Zyy + y Zy. %3D

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Q: dy + ydx %3D 3x²y?dx,

A: Given differential equation is bernaulli's differential equation.,  and we can solve it by reducing…

Q: A continuous r.v. F(x1= === 2 × -IN 15 X has CDF X Co OBX C1 18X 16 17 **** 18

A: Given: Fx=0            x<012x        0≤x<1k            x≥1

Q: of and dy For the function f(x,y) = In (8x + 9y), find - - of

A: partial derivative of two variable functions

Q: 25. For y = f(x) = x2 - 3, x = 5, and Ax = 0.1, find Ay and f'(x) Ax. %3D

A: Given: fx=x2-3 ,x=5 and ∆x=0.1

Q: x - y -2x Prove by definition that for f(r, y) fy(x, y) = %3D x+ y' (x+ y)2

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Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: If f* f(t) dt O 6 1 O -4 divergent = 20x √4x²+21 ∞ -4, then f(t)dt is X

A: Given

Q: Find D,y, given y = 3e" (2x – 5)*. D.y = 3e [4(2x– 5)'(2)]+(2r-5)'(3e") = 24e" (2x – 5)' + 3e"…

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Q: Determine the linear approximation of f(x) = x' at x = 1. О а. уз- 1 х-0 О Б. у3 1x +0 O c. Not in…

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Q: Let f (x,y) =In Then f „(1, – 1) =... 3x²+ 4y3

A: This is a problem of partial.

Q: of of and ду Find f(x,y) = Vx + 3y?

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Q: 6) If y=x² +1+ f dt , prove that y"= 2 - x2

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Q: The function S(x.y)= (2x* + y^ )exp[ y + xy' is homogenous in x and y of degree 2x

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Q: Determine the linear approximation of f(x) = =ª at æ = 1. O a. y=- 4x-3 O b. Not in the list O c. y=…

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Q: Let f(x, y) = ln (3x + y2). Show that fxy = fyx

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Q: Find x' for x(t) defined implicitly by x+t°x+t -8=0 and then evaluate x' at the point (-2,2).

A: x3+t3x+t4-8=0Differentiate w.r.t…

Q: Find x' for x(t) defined implicitly by x +tx+t° - 5=0 and then evaluate x' at the point (- 1, - 3).

A: Follow the procedure given below.

Q: Verify that the indicated function y = p(x) is an explicit solution of the given first-order…

A: This question can be solved using the concept of derivatives.

Q: of Find of and for the following function. dy 5x f(x, y) = 10y 4y 3x

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Q: 9. f(x.y. z) = In(x + 2y² + 322); P(-1, 2.4): u = -i- j - k

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Q: Compute the first-order central difference approximations ofO(h^4) of t function of y at x = 1h =…

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Q: Find f, and f, for f(x,y)=y In (3x +4y). fx fy

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: (b) Show that the function f(z) = ez, z = 0 and f(0) is not analytic at Z = = 0, although C-R…

A: The given function is fz=e-z-4=1e1z4 To show: f(z) is not analytic at z=0 and f satisfies C-R…

Q: 1. Integrate the function f(x, y) = x – y over the triangle T with vertices (0,0), (1,0), and (1,2).

A: Given triangular region is bound by the vertices 0,0, 1,0 and 1,2. The sides of the given triangular…

Q: (b) For f(z) find the residue of f (z) at the singular point (z+1)2(z2+4) z = -1

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Q: (b) If F = (5xy- 6x )i + (2y– 4x)j, Evaluate [F.dr along the curve C in the xy-plane, y =x' from the…

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Q: -2 In(x) Consider the function f(x, y) 3y

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Q: If f(x, y, z) = In(x³ + yl² + 2®) + V (x12 + y6 + 23), then find fr, fy and f; at (1, 1, 1).

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Q: (ii)If y=(x+Jx* +1. prove that y'= Vx +1

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Q: Let f1(x, y) - e cos(5y), f2(x, y) = x² – 25 y². Find Vf, and Vf2, and show that %3D (fv) = 0 for…

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Q: Is the function u(x, y) = -3(g + 1)x²y+ (p+ 1)y³ harmonic? If your answer to the last question was…

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Q: 4. For the function f(x, y) = exp (ax + by) find the maximal possible value of the directional…

A: In this question we will use basic of calculus i.e concept of vector calculus. We will find the…

Q: 2. Show that the function u - p(sy) + Vj (y/2) provides the equation 0.

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Q: if f(x)=integral t^3+5t^2+6, from 0 to x. what is f''(x)=?

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Q: Q3: Find fxx of the function f (x, y, z) = -In/1-x2 - y2 – z2 %3D

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Q: 2. Let f(x,y) 3x y. If C is the line segment from (1,1) to (2,3), evaluate r'dt.

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Q: Which of the following functions has a maximum y value of 4 Oy= 4cos x y= cos 4x Oy= cos x + 4 Oy=…

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Q: 1. Find the local extremum of the function (a) f(x,y) = 2x² – xy + y² – x – 5y + 8 %3D (b) f(x,y) =…

A: *As per Bartleby Policy, only first question answerd. for remaining questions, please repost it as a…

Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

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Q: Show (in terms of e - 6) that a function f : R → R defined by f(r, y, 2) = (2x + 3y + 42) is…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.