Find eauation of ny Perbola at o Ne tne foci Fz the and crankshafto f Fi Fz ny Perbola= Fi F

Q: Find the arclength of y = 2a/2 on 1 <a< 2

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Q: Find the solutiTon of followina ordfnarg differentral equation -2x

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Q: The length of the curve y = 3 - 4Vx for 0 < x < 3 is calculated by the integral: %3D Select one: 3 O…

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Q: Let L be a tangent line to the hyperbola xy=4at x=7. Find the area of the triangle bounded by L and…

A: Given: L is a tangent line to the hyperbola xy=4 at x=7. To determine: The area of the triangle…

Q: vesify Gxeen't theosem 6 (2x+34)dx. tey -x)dy whese cathe Vesticas C0,0) (2,0) (2,2) and (0,2).…

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Q: Find a parametrization of the right branch (x &gt; 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: Find a parametrization for the cylinder x^2 + y^2 = 4.

A: Given: x2+y2=4

Q: 7. Derive the orthogonal trajectories of the family of hyperbolas xy = c. %3D

A: The solution are next step

Q: 2. Find the divections..in.w.hic . fCx,y) = X- a.. Increases.ms..rapidly.at. paint.C1). b. Decrenses…

A: Solution: The given function is fx,y=x22+y22    ......(1)

Q: Q2\ Shoe that another from of Euler- * Lagrange equation is : L, -L,½ -y'L,ý - y"L,51 = 0 . - y 'Ly5…

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Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: Find y': y arcsin Oy =-- %3D Oy = - zV-9 %3D Oy = %3D zV-9 %3D -69

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Q: Tangent to the parabola z = x² + 3y² , x = 1 , at point ( 1, 2, 13

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

Q: Find the path of a heat-seeking particle placed at point P on a metal plate whose temperature at (x,…

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Q: Find the arc length of y = -6x + 2 on [2,5] (use calculus). %3D L = 1 + f'(x)² dx

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Q: Find the exact value of | (yi+ vxj) · dr where C is the parabola y = x² from the origin to the point…

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Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: Use Green's theorem to evaluate (2y dx-x dy) around the closed curve C. 27 (2,8) 8. 4. C. -2 (1,-1)

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Q: Find a parametrization of the osculating circle for the parabola y = x2 when x = 1

A: It is given that, y = x2.The parametrization is, r (t) = &lt;t, t2&gt;That implies,

Q: Determine the so luti'on of the equertion: dy dx2y cot x= 1- 2xcot 2x- 2csc 2x

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Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

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Q: A-Estimate J, 2e-3* dx using trapezoidal rule with four subinterval round your answer to one decimal…

A: Given is the integral  ∫-11 2e-3xdx The aim is evaluate the integral using trapezoidal rule.

Q: DNE.) +2+ f defined on |-1,3] maximum (x, y) = minimum (x, y) = Need Helo?

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Q: tion z2 – (x2 + y2)2 and let p = (0, 0, 0). ermine the set Tp(Zf ) of all tangent prs to Zf at p. Is…

A: Sol

Q: Find the tangent plane to the equation z 2y cos(3r - 6y) at the point (6,3,6) %3D

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Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

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Q: * Find the length of the curve.7 (ähäs 3) f(x) = In(sec x) %3D 4 In(3 + 1) O In(3 + 2) O In(2 + 2) O…

A: Hence option (d) is correct.

Q: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

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Q: 1. Tangent to the parabola z = x + 3y?, x = 1, at point (1,2, 13

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Express x = In(3t), y = 5 – t in the form y = f(x) by eliminating the parameter. %3D y =

A: Given that x=ln(3t) and y= 5-t we need to write y=f(x) by eliminating the parameter  Now , x= ln(3t)…

Q: Show that the arclength of the graph of y = sin x on the interval [0, 27] is equal to the circum-…

A: The length of the smooth curve ζ : [ 0 , 2π] →ℝ2  is given by I(ξ) = ∫02π ξ'(t)  dt

Q: Evaluate I C: arc on y = x³/2 from (0, 0) to (4, 8) (2x −y) dx + (x + 3y) dy.

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Q: a Use parseval's identity to prove that dt TC (a² + )(b + ?) 2ab (a + b)

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Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: cos(u) dx. int_ccC [2x*cos(y) \ dx \ - | x^2 sin(y) \ dy] x? sin(u) dul if C is the curve x^4+y^4=1,…

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Q: Suppose that the Celsius temperature at the point (x,y,z) on the sphere x +y +z =1 is T= 1600xyz“.…

A: This is a problem related to maxima and minima. Based on the general formula we will answer the…

Q: Find the Arc Length. y=2/3(x2+1)3/2, 0≤x≤1

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Q: Starting from the point (-4, 5, 4) reparametrize the curve r (t) = (-4- 3t)i + (5 – 3t)j + (4 + 2t)k…

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Q: Integrate h(x, y) = (x+y)i+-x)j over the closed curve that begins at (-1, 0). goes along the x-axis…

A: Let me tell you , In this problem we are going to use Green's theorem. Note: Green's theorem is only…

Q: of the solid in revolution as it axis and the function 2 – x) 0<x< 2

A: The given function is fx=x2-x,    0≤x≤2. Find the volume of the solid in revolution as it rotates…

Q: 10. Find the surface area of the solid generated by revolving the line segment y = vx + 1 , 1 < x <…

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Q: Find the length of one arch of the cycloid x= 6(t-sin(t)) y= 6(1-cos(t))

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Q: Let C be the closed curve starting at (0, 1) traveling along the parabola y = (x – 1)? up to the…

A: Using Green's Theorem we solve the above question.

Q: (a) Show that y = x* is concave upwards at the origin and y= e* is everywhere concave upwards.

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Q: Find the arclength of y = 2x +1 on 0 < 1< 3

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Q: find enit vect in the d a most ropidly at in which f increase P and find the yoate of charge of f at…

A: The objective is to find a unit vector in the direction in which F increases most rapidly at P and…

Q: TQand TR are secants from Point T to Cirlce A as shown below: s. If mQR = 70° and mSP 34°, what is…

A: Given: To explain the correct of the given statement as follows,

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.