Two parameterizations Verify that fc (x – 2y + 3z) ds has the same value when C is given by r(t) = (2 cos t, 2 sin t, 0). for 0 sts 2m, and by r(t) = (2 cos f, 2 sin t², 0), for 0sts V27.

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Q: In Exercises 35–40, find the partial derivative of the function with respect to each variable.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please re…

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A: Solution is attached

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A: We use the concept of exact differential equations to find the general solution to given…

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A: We have to find

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A: Formula used: Midpoint rule- The interval [a,b] into n subintervals of equal width,…

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Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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A: We will find out the required solution.

Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: Q1: If Z = x³ + y* + (x sin y) + (y cos x), Find Zx/Zy?

A: We are given: Z=x3+y4+(x sin y)+(y cos x)To find: ZxZy This can be calculated as follows:

Q: (a) f(x) + cosh(47) (b) f(z) = VI In(|tan(9r)|) tan n(x) psin(z) 12 (c) y = dt

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Q: Let f(x, y) = x² + y² and r(t) = (cos 1, sin t). (a) Find f(r(1)) without making any calculations.…

A: a) Equation of the circle with the centre at the origin that is (0,0) is x2+y2=a2 then every point…

Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x : y = 4t t' Enter…

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Q: let y(t) be a solution of (cos y + 1). dy = 2t such that y(2) = 0. dt Show that sin y + y = t2 + C.…

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Q: The value of f(z) = e² at z = 3 + 4i in terms of x + iy is O a. 1 O b. e cos 4+ie sin 4 O c. e*…

A: Given, We have to find the value of  fz = ez  at  z = 3+4i  in terms of  x+iy  .

Q: ds Find the function s(t) satisfying = 4 -9 cos t and s(0) = 7. dt

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 9 cos x – sin xy; x y = 2t t' Enter…

A: This question is based on Derivative.

Q: af ar fe Consider f(1, y, z) = r² + y²z² and I=r sin 0, y =r cos 0, z = Or³. Find and

A: The function fx,y,z=x2+y2z2 and the polar transformation coordinates are x=rsinθ, x=rcosθ and z=θr3.…

Q: Which of the following is equivalent to u=-cost+v3 sint ? a) u = 2 cos t +- 1 b) u = – cos| t+ 2 3…

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Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find fx(8,9,0). Leave your answer correct to two decimal…

A: Solution

Q: Given that r = 3 cos nt, y = 3 sin at and z 4nt with 0<t <1. Evaluate (x+ 2) ds.

A: The line integral is defined as,

Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) Oe2 0 0 O cos 2 O-sin 2

A: The given function is: fx,y=excosy   As we know that; The common derivative; ddxcosx=-sinx And…

Q: 1. e+sin z- COs I 2e-u(t)dt

A: Part(1):-

Q: Q1. If f(x,y, z) = cosh?(Vx² In y) + tan-(e2y²vz) + sec³(sin vVE In x²) Find fx, fy, fz» fyx

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Q: Find r(t) for r'(t) = 2/ti + 3 cos(2nt)j – e-'k and the initial condition r(0) =i+2j

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Q: 2. Give an interval of the form (a, b) around r 1 such that the IVP has a unique solution. dy = sin…

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: Find the value of integral | (22 + y² + 2)ds, where C is parmeterized by F(t) = (cos(4t), sin(4t),…

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Q: Given the implicitly defined function 6. cos (2*y) – y* - cos(2r) – y? dy and dr dr find at the…

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Q: • T/4 cos(0) f |/| f(x, y, z) dV = 9p sin(ø) cos(4) dp d0 dø, find f(x, y, z). E f(x, y, z) =|| ?

A: We have to given ∫∫∫Efx,y,zdV=∫0π2∫0π4∫0cosθ9ρ2sinϕcosϕdρ dθ dϕ Now the function which is to be…

Q: cos(x) If f(x) = ["(@) "g(x) V1 + t3 dt, where g(x) = S [1 + sin(t²)]dt, find f'(;). 1 %3D

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Q: Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give…

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Q: Given f(x,y) = ex cos y, Evaluate fy(0,2) A cos 2 B) e² CO (D) -sin 2

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

Q: Q2: find dw/dt at given value point for the following function x= cos°(1), y = sin²(1).= =-. 1 at t…

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Q: ds Find the function s(t) satisfying = 6 +5 cos t and s(0) = 5. dt

A: It is integration using initial conditions.

Q: f(æ) = / t2 – 9 dt 1+ cos? (t) At what value of x does the local max of f(x) occur?

A: Given: For the local maximum value of f(x), we must have f'(x) = 0. Here,…