QUESTION 3 Evaluate fds, where f(x,y) 2x +3y and C is the counterclockwise curve around the circle X+y= = 4 from (2,0) to(-2,0).

Q: Q46) Use shifting graph to sketch a) y = |1 – vx|- 3 b) y = -1+ sin (x – 0.5)

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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 1 Consider the curve defined by 2y3 + 6x2y - 12x² + 6y = 1. dy 4х - 2ху (a) Show that dx x2…

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Q: Question 12 Find the moment of inertia of the region between the parabola y = 9 - x2 and the line y…

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Q: Chapter 12, Section 12.3, Question 006 Find the arc length of the parametric curve. x = 6 cos t, y =…

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Q: Question 3 Express the curve by an equation in r and y given r(t) = sec² (t) + 2 and y(t) = 5 +…

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Q: Find the horizontal and vertical asymptotes of the curve

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Q: 15. Suppose you start at the point (0, 0, 3) and move 5 units along the curve x = 3 sin t, y = 4t, z…

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Q: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: Question 3 Find the tangent plane to the equation z 3r - 5y + 5y at the point (- 5, 2, 65). Submit…

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Q: 5. f(x) = - x/² on (0, 1].

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Q: Question 2 Find an equation for the line tangent to the curve at the point defined by the given…

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

A: Line integral

Q: Question 16 Find the equation of the tangent plane to the given surface at the indicated point. x2…

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Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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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: Q.18 A curve 'C'is defined as x= a cos³0, y = a sin°0 in [O, t/2]. What will be the point P on curve…

A: Explanation of the answer is as follows

Q: 7. (~Ch16 Review #6) Compute y3 dx + x² dy where C is the arc of the parabola x = 1- y² from (0, –…

A: In this question we need to find the given line integral .

Q: A curve C is given parametrically by x = cos(t) - 2 and y = sin(t) + 3, where 0 ≤t≤ 2π Find and…

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Q: Question 8 In(t2 + e2)- 2 lim t 0 (a) 0 (b) 1 (c) 1/2 (d) 2 (e) none of these Question 9 The slope…

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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: Find the equation of a line normal to the curve of y= cos at x= 1. Select one: A. -33 x + 9y - 9 +…

A: Equation of Normal

Q: Find the arc length of the graph of the function over the indicated interval.

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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: If f'(x)=/cosec*.x-1 then what is the arclength of the curve y= f (x) on 3 2 B) 3 D) 3 E) V3-1 A) 1…

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Q: 9. Find the exact length of the parametric curve for the given interval. x = 4t 2 - 3, y = 3t, 0 St5…

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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: 3 4. Find the arc length of the graph of the function f(x) =;(x² + 1)ī over the interval [0, 1]. =…

A: y =f(x) =23(x2+1)32f(x)=23(x2+1)32f'(x)=23*32(x2+1)12(2x)f'(x)=(2x)(x2+1)12 The Formula for arc…

Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: A heat-seeking particle has the property that at any point (x, y) in the plane, it moves in the…

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Q: Problem 8. Find equations for the tangent plane and normal line at the point Po on the given…

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Q: 3 6. Find the arc length of f(x) = G (x2 + 2)z on the interval [0,9]

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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: I grad(f)•dr where C is graph of y = x² + 3x from (0,0) to (2, 14) and f (x,y) = ev/lx*•1}

A: The function is fx, y=eyx+1. Find: ∫Cgradf·dr…

Q: Graph the Plane Curve defined by: I = 3 cos(t) - t + 5. y = sin(t). for t in [0, 37]. x Clear + Undo…

A: Plot the points for different values of t from [0,3π]. Draw the curve passing through the points.

Q: 3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

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Q: Find the Giniindex for the lorenz curve L (X)= 0.3X + O=7X 11

A: Given the Lorenz curve Lx=0.3x2+0.7x. Find the Gini index of the Lorenz curve.

Q: A curve is written parametrically with x and y defined as functions of t: x=t2 +1, y = 4r° +3. Find…

A: Take the derivative of x and y with respect to t then use the formula for the arc length.

Q: Question 2 Suppose an object is moving along the unit circle. (æ(t), y(t)) Find the correct relation…

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Q: QUESTION 5 Calculate F.dr if F=(sinx,x²y³) and C is the triangle oriented counterclockwise with…

A: Solution is given below

Q: Question 1 If Ø = x?yz³ and A = xz i -yj +2x² yk Find the vidergence at (1,1,2).

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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: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

Q: Let curve C be the arc of x2 + y2 = 16 traversed once counterclockwise from (0, 4) to (0, -4). Let…

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Q: 6. The curve C: 3*-1 + xy - y? +5 = 0. show that at points (1,3) can be writien in the form -In(ue)…

A: Solve the following

Q: Question# (3} Set up the integral that gives the arclength of the curve: f(x)= tan(x) for 0<x<“ . 4…

A: Will use the arc length formula to set up the integral

Q: 7- A sinusoidal curve has a minim um point at (-t/3, 5) and the closest maximum point to the right…

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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: Find the isogonal trajectory of the family of curves y + 2xy – x² = k where tan a = 1

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.