Determine wheter f and are învers L41) f(x) = x-2, glx)=

Q: Find the work done by the force F = 4xyi + (2x² – 3xy)j by pushing a particle along the line segment…

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Q: (a) Use the trapezoidal rule to approximate the integral. dx

A: Solution of given question is written in below steps.

Q: Compute fx + fxy + fyyzz, where f(x, y, z) = z sin(xy)

A: Given f(x,y,z)= z sin(xy)

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

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Q: Use Green's Theorem to evaluate the line integral

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Q: 5. Using tangent line approximation, approximate the value of: a. V9 b. 3.012 – 4(3.01) + 7

A: The objective is to tangent line approximation to approximate the value of 3.012-43.01+7

Q: Find the tangent to y = cotx at x = - T O A. y = - 2x + 2 π +1 +1 OB. y=2x-- OC. y=2x+1 OD. y=-2x +…

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Q: Find the tangent plane (Xo, Yo, Zo) from f (x, y) = x² - 3y²; (0,1, -3)

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Q: Find the plane tangent to f(x,y)=x/(x+y) at the point (1,5).

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Q: Find the Contour integration to

A: ∫-π-π11+sin2xdx∫aafxdx=0, a≠∞=0

Q: bounded by the curve f(x)= Vx-1, y-axis, line y =1 and line y =

A: We will find the area bounded by the curves.

Q: Use linear approximation to find y = L (x) of the function f (x) = = COS X about the point xXo = JT…

A: Use formula of  linear approximation

Q: rea under the curve y = 2x – x² from x = 1 to x = 2 with n = 4 %3D tonglon

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Q: Let f(z) = z2 is f(z) satisfy Cauchy-Riemann equation ?

A: Let any complex function f(z) = u + i v then it satisfies Cauchy-Riemann equation when 1) ∂u∂x=∂v∂y…

Q: Find the linear approximation of the tunction fox) = NT-x at a-0 %3D and use it to approximate the…

A: We find f'(x) using the power rule.   then we find f(0) and f'(0)

Q: UNIVERSIT b) Given z = f (x – y, 2x – 2y, 3x – 3y). Show that - dz dz + = 0. dy

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Q: 6) What is the tangent plane of f (x, y) = 5x² – 2xy? + 3xy + 4x at point (xo, Yo) = (1, –2) ?

A: The question is solved in step. 2

Q: Integrate f(z) over unit circle C and indicate whether Cauchy's theorem may be applied (4) f(z) =…

A: With the help of Cauchy theorem of integration we solve this problem.

Q: Show that f(z) = x ² + y ² where z = x + iy is not analytic anywhere using Cauchy Riemann equations.

A: Cauchy Riemann Equations: Given,  f(x+iy)=u(x,y)+iv(x,y)  and it should satisfy  ∂u∂x=∂v∂y and…

Q: find the to the the tang horizontal. X-volves at which the _9x+2 Y = ex curve ent

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Q: bounded by Y=x3, V=1x i rotare about X=1

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Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

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Q: find a potential function for F or determine that F is not conservative. F=(z,x,y)

A: F is conservative when curl F = 0 Given that f=(z, x, y)=zi+xj+yk

Q: Find for the equations for tangent plane and normal line at P,on the given surface 2 х2 — Зху — у?…

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Q: e moves along line segments from the origin to th F(x, y, z)=z²1+ 3xyj + 2y²k. work done.

A: In this question, the concept of line integral is applied. Line Integral The function to be…

Q: express the length of the curve as an integral but do not evaluate it. r = (2 − cos θ )−1, 0 ≤ θ ≤…

A: Definition used -                Length of the curve -            L=∫αβrθ2+r'(θ)2dθ

Q: Evaluate fs xyz dS where S is the triangle with vertices (1,0,0), (0, 2, 0), (0, 1, 1).

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Q: Find the approximation of the integral. 1= [e*dx Using Romberg's rule derived from Trapezoidal rule…

A: Given integral I=∫01e-x2dx Here we use Romberg's rule derived from Trapezoidal rule for 1,2,4,8…

Q: Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.

A: A function is called differentiable, if the derivative of function exists at each and every point in…

Q: Use trapezoidal rule to estimate the the integral. V + Adx n=6 a) 2.75

A: the given integral is ∫14x2+4dx given n=6 therefore  h=b-an=4-16=36=0.5

Q: (a) If f(x,y) = e" siny – e sinx then verify that fæy = fyx. %3D -

A: Given that  f(x,y)=e^xsiny-e^ysinx To verify the fxy=fyx

Q: The tangent plane to the graph of the function f(x,y)=x+xy+y2, which is parallel to the z=1+2x+3y…

A: Here given surface is fx,y=x+xy+y2 or x+xy+y2-z=0......1 Then, consider Fx,y,z=x+xy+y2-z

Q: a) by parametrizing C, b) by using the Fundamental Theorem of Line Integrals.

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Q: Find the tangent plane of the function f(x, y) = √2x² + 2y² at (1,1). Is it parallel to 2- the plane…

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Q: Find the limits of integration in cylindrical

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Q: ) Compute f-(, ") and fy(§, T) of f(r, y) = e9 cos(ry)

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

Q: Scos* y sin ydy

A: Given problem:- ∫ cos4(y/2)sin(y/2) dy

Q: Derive the error term of composite trapezoidal rule for integrating S f(x)dx.

A: ok, let us say that we are dividing this region in n regions,

Q: 2dy -2y 2. zt at

A: Solved below

Q: A plane area is bounded in the first quadrant by the curves y² = -16 (x-4), the line 8x-15y = 0, and…

A: Given the curve is y2=-16x-4 and the line 8x-15y=0 and x-axis. We have to find the moment of inertia…

Q: Use the Chain Rule to find dQ where Q=√√3x² + 3y² + 4z², x= sint, y = cost, and z= cost. dt'

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Q: Inx F (x) = So It dt %3D

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Q: What does parseval's identity imply about relationship between the dot products x · y and [x]ẞ·…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: Find the limits of integration with respect to u and v

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Q: Use a linear approximation to estimate V29. Show the work. Do not round your

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Q: The orea bounded by the curve y=- ond the line xty=3 is equal to ?

A: The given curve is ,  y=2x...........(1) and the line x+y=3...........(2) we have to find area…

Q: sin x dx B) - 7 1+ 2 1+ A) -(1+ 2) 7 C) - 2 1+ D) 4 8

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Q: nit vector that is parallel to the

A: Here have to find the unit vector that is parallel to the line tangent to the parabola y = x2 at the…