QUESTION 5 Calculate F.dr if F=(sinx,x²y³) and C is the triangle oriented counterclockwise with vertices at (0,0), (1,0), and (1,1).

Q: Question 25 Solve the problem. Write parametric equations for the tangent line to the curve of…

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Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

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Q: Question 14 Solve the problem. Find the equation for the tangent plane to the surface z = 8x2 - Sy2…

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Q: Which one of the following points lies on the curve r = sin 0 – 5. o (-5, T) -5, o (5, 2n) o (5, 0)

A: Given r=sinθ-5 if θ=π, Then r = sinπ-5 = 0-5= -5 therefore, (r,θ)=(-5,π)

Q: Question:2 Find domain of following functions S(x, y) = In(e*+e") arctan(x+y) а. f(x, y) = b. ( x² –…

A: The function in a will not be defined when x+y=0.  Thus, domain is:

Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: Question 1 Which of the following sets of functions are linearly independent on (0, ∞)? O {1, tan²…

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Q: Question 9: Calculate r (t). r (t) = (4t, 2e2t + 1, 2 sin(t)) ®F(t) = (4t, 2e2ª – 1,2 sin(t)) O F(t)…

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Q: Find f and f and evaluate each at the given point. Mx, V) = arctan(2). (6, -6) ,0x. y)= ,0 y) =…

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Q: QUESTION 7 Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the…

A: Given that  Z=x^2+2y^2  Point (-1,-1,3) To find teh point lies in p

Q: QUESTION 1 Calculate F.dr if F=(sinx, x'y) and C is the triangle oriented counterclockwise with…

A: Line integral

Q: Graph the following vector fields

A: (a)known fact:

Q: QUESTION 6 Consider the function f(r, y, z) = 6x² + 4xy+ e4yz af Then is equal to: ду O A. 4x +…

A: we find out partial derivative with respect to y.   see 2nd step.

Q: a) Determine an equation for the sinusoidal function shown. c. y= 0.5cos 0.5(x+ )] + 1.5 d. y=-cos[…

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

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Q: Question #2) Find the absolute extrema when f(x,y) = xe – x² – e :R is the rectangular regioi with…

A: Both questions are independent to each other so according to the guidelines , I am solving first…

Q: Question 6. Let u := Vr+ 82, with r:=y+x cost and s := x+y sin t, with t, x, y € R. [6] Determine if…

A: Here we use basic rule of chain rule

Q: Question 6 Find the unit tangent vector T (0) to the curve C: r (t) =2 cos(t)i +3 sin(t)j+ 4tk ©T…

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Q: b)A hanging chain has the b)F Shape y=3C0sh(3x), o 4X sIn2 calkulate the lengnt of the chain.

A: Length of chain is the same as length of curve

Q: Calculate and graph the tangent of the function b) r = -6ecose + 8 cos 40 5T 0 = 4 %3D in

A: Given that, r=-6ecosθ+8cos4θ and θ=5π4

Q: Question 1 Specify and sketch the domain D(f) of the following function sin(x + y) Va2 – y² + 1 f(x,…

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Q: Question 14 Find the equation of the tangent plane to the surface y = 2x2 – (0,-1, –2) z2 at the…

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Q: Question#4: Use Green's theorem, evaluate | F.dr for the following function: а : F = grad sin x cos…

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Q: Question 11 Let C be the path given by the parametriç equations Xt and y -1from t=0 to t=2 and let…

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Q: Question 3 Find the value of J sinydx+ (xcosy-sinyldy, where Cis any curve from (2,0) to (1, T). Ca…

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Q: QUESTION 5 Evaluate F dr, where F(x,y)=[2y-3cos(x)]i + [4x +6sin(y)]j and C goes counterclockwise…

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Q: Question 1 described by the vector function r(t) = (4t² ln t, ¹-4, -2e-3t). 2 a) Consider the curve…

A: Given: Vector function rt=4t2lnt, t-42, -2e-3t. a. To find the integral ∫rtdt. b. To find the…

Q: u(x,у)- (sin x)(e' — е").

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Q: (c) h(r)- (r- 2r)(r+) (d) j(r)= COS T 1- sinr *cos2tan r (e) f(r) Page 2

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Q: Question 8: The curve C in the ry-plane is parameterized by r (t). Find a parameterization of the…

A: Given:r→'t=4, 4e2t, 2costr→0=0,1,0

Q: The equation for the sinusoidal graph below is: f(x) = 4sin(2x) 3sion (2) 1 f(x) = 3sin f(x)=2sin…

A: Given is a sinusoidal graph.   To Choose: The correct equation for the sinusoidal graph

Q: Question 3 Find the point(s) of intersection of the curves r = 6 and r = 12 sin e OA 6 * (6.5)(6) 3…

A: To find the intersection of the curve r=6 and r=12sinθ

Q: QUESTION 14 The equation of the tangent plane to z=f(xy) =x² siny at the point (1,0,0) is given by…

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Q: au, a'u +: Q3) A: Find u = In(x + y) + tan () where

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Q: Question 2 Express the curve by an equation in z and y given z(t) = cos(t) and y(t) = 3 sin(t). a)…

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Q: Find f and f, and evaluate each at the given point. () (4, -4) f(x, y) = arctan %3D f(x, y) = f,x,…

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Q: Question 8 Find the coordinates of the point(s) on the curve y = Va + 4 that are closest to the…

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Q: Question 10. Find the angle between the curve r(t) = (t, sint, cos t), and the curve y + z2 = 1, x =…

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Q: Question 1 described by the vector function r(t) = (4t² ln t, t-4 29 -2e-³t). a) Find the integral…

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Q: Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x…

A: We have to find

Q: Find the general solution to the hypergeometric ODE #(1 – 2)y" + (; - 2-) a - - 0. 3 ) y y = 0.

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Q: A weight suspended from a spring is pulled down a distance of 6 ft from its central position, then…

A: Given that a weight suspended from a spring is pulled down a distance of 6 ft from its central…

Q: Question 1 Let r (t) = (sint – cos t, 3t, sin t + cos t) , t >0 denote the path of a particle in…

A: Unit tangent vector , T(t) = r'(t)r'(t)

Q: Question 10 described by the vector function r(t) = (4t² ln t, ¹-4, -2e-3t). Find the integral ſ…

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Q: Question 4 azu a?u (a) Verify that u satisfies yz = 0 , if u = e*sin y. +

A: Dear students as per guidelines we answer the first question only when multiple different question…

Q: Find the cartesian equation of the curve

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Q: Question 2 Consider the function f (x, y, z) = x² + y' – xyz Find the equation of the plane tangent…

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Q: Question 2 Find the length of the curve r(t) = (3 cos t)i + (3 sin t)j + 2ek, Osts3.

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Q: 6. If r = and 2+ cos 0 (c, 0) is a focus expressed in rectangular coordinates with c+0 then c =

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Q: Question 1 Write acceleratin a in the form of a = arT +aNN without finding T and N. (a) r(t) =…

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