3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 = 0 and show that r = r at that time.

Q: Suppose that C is the curve defined by the polar equation r = 2+4 cos 0 (called a limacon). opose…

A: Find the attachment for the Solution.

Q: Deduce from the orbit equation (1 + e)r 1 + e cos 0 that a planet is closest to its sun when 0 = 0…

A: Here,  r=(1+e)r01+ecosθ differentiate with respect to θ

Q: 4. Evaluate 2.x cos y dx – x sin y dy along the elliptical path + y? = 1 from (2,0) to (0, 1)…

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Q: 1. Find the equation of the tangent line (s) to the following set of parametric equations at the…

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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: A curve is defined by the parametric equations a(t) = 2 cos(5t) and y(t) = -7 sin(-10t). Find .

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Q: 12/2 Use polar coordinates to evaluate dydx. 3 0. (x² + y²)²

A: To convert cartesian coordinates to polar coordinates , put x=rcosθ, y=rsinθ , dydx=rdrdθ So,…

Q: D Eolm the secend order diffefential equation using the parametric delinitien of y=asine X-a Cos e…

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Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

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Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: 5. Eliminate the parameter to find the equation of the ellips Sx(t) = 4 cos(t) + 1 ly(t) = 3 sin(t)…

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Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

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Q: dy = cos 20. de dx Given that r= cos 0 ; = - sin 20 and de The slope of the tangent line to the…

A: Given that: r=cosθdxdθ=-sin2θdydθ=cos2θ

Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: A slime mold grows in a spiral pattern with polar radius r=θ3r=θ3. If the mold grows by continuing…

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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: Find the slope of the polar curve r= e® at 0 = n/3.

A: Given:

Q: 3. Find T (t) and a set of parametric equations for the tangent line to the helix given by ř(t) = 2…

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Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

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: 11. dy/dx = -x/y, y(0) = 4 %3D

A: Given: Let's sketch the isoclines and their direction markers, then sketch a few solution curves,…

Q: Consider a particle traveling clockwise on the elliptical path                              x2/ 100…

A: Given: x2100+y225=1  or  x2102+y252=1 Leaving point of the particle from the orbit (−8,3)

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

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Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Find the exact length of the polar curve described by: r = 5e-0 %3D 7 on the interval

A: The given function is r=5e-θ, where  7π2≤θ≤6π. The length of the polar curve is obtained by the…

Q: 4. Find the exact length of the polar 2 cos os 0, 0 < 0 < T. curve r

A: Given: r=2cosθ on 0,π L=Length of Polar curve= ∫ab(r(θ))2+(r'(θ))2dθ now, r'(θ)=ddθ(2cosθ)=-2sinθ…

Q: 3. Draw a hyperbolic orbit with of a =1.0, eccentricity of at (x, y) = (-1,0). the semi major oxis…

A: Solution:   Equation of hyperbola is given by (x-h)^2/a^2 - (y-k)^2/b^2 = 1 focii is at (h ± ae, k)…

Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: 4. Calculate the arc length of the polar curve r = e38 from 0 = 0 to 0 = 2.

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Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: Deduce from the orbit equation r=(1 + e)r0 /(1 + e cos u) that a planet is closest to its sun when u…

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Q: Find the exact length of the polar curve

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Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

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Q: Suppose an object moves in an elliptical orbit parametrized by x = 4 cos t and y = 5 sin t, where t…

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Q: au +20 dy 10 www ax dy dy?

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Q: Find the exact length of the polar curve described by: r = 5e-0 1 on the interval T <o< 9n. 10

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Q: 1. Use the parametric equations of an ellipse, x = a cos 0, y = b sin 0, 0 < 0< 27, to find the area…

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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: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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Q: 7. The polar equation of the curve r2 + y² = 2x is A T= 2 cos 0 T= sin 20 T= 2 sin 0 B D T= cos e

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Q: Prove that e dz < ++1 3 where C is the arc of the circle |2| = 3 from z = 3i to z = -3.

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Q: Consider the curve C of equation: (x² + 2y + y²)² = 4(x² + y²). From the following options choose…

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Q: (e) Graph the surface in R' whose spherical equation is p = cos 20.

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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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Q: a. Find the solution set for log, 2+2.log3 x= log, (7x-3) b. Plot the polar curve r 2(1-cose) in…

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Q: Find the exact length of the polar curve described by: r = 7e-0 3 on the interval 10

A: r=7e-θ,    310π≤θ≤6π Differentiating with respect to θ, we get drdθ=7-e-θ=-7e-θ