9. The Cartesian equation of the curve r=- is 1-cos(0) (Write your answer in the following form y?= ...) 18x + 81

Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

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Q: (a) The curve with equation y 2   = x3 +3 x 2  is called theTschirnhausen cubic. Find an equation of…

A: We find dy/dx at x=1 and y=2  So the slope of the tangent = 9/4

Q: ind an equation of the tangent to the curve at the given point by both eliminating the parameter and…

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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: 4. a) Find the entire are length of the curve r = 2a cos³ (0/3).

A: 4a Given curve is r=2acos3θ3. We have to the entire arc length of the given curve. The entire arc…

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: 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: 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: the equation of the tangent line to the curve y = 4 sin x at the point equation of this tangent line…

A: We are asked to find the tangent line of the curve.

Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

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Q: oblem 1. (a) A curve is defined by the equation 2 sin(y) – xy + y² = 0. Verify that the curve passes…

A: Given, The equation of the curve 2siny -xy +y2 = 0  Curve is passing through the point π, π  We have…

Q: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint); + In…

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Q: Find the equations of the lines that are tangent to at the origin the curve X cos t, Y = 0.5(sin 2t)

A: Please refer the attached image for complete solution.

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: An equation of the kangent and hormat. X+sinx líne to khe curve Y =xê

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Q: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: Find T, Ñ and B for the curve 7 (t) = (5 cos(4t), 5 sin(4t), 2t) at the point t = 0 Give your…

A: the given curve is  r→(t)=5cos(4t),5sin(4t),2twe have to find a) T→(t)=unit tangent vector at t=0b)…

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: 9/Find Parametric equations for the Line that is tangent to the curve r(t) = eti + (Sint)j + In…

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Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

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Q: 1- Find the equation of the tangent to the 2(x2 + y?)2² = 25(x² . y?) %3D at (3,1)

A: To find the equation of the tangent

Q: 50 Find the length of the curve whose equation is given by r = e on 0 < 0 < 2T.

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Q: 1. Consider the curve given by the equation y3 – xy = 2. It can be shown that dy %3D y dx 3y2-x (a)…

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Q: Q2:Is the point lies on the curve? x² cos y – sin y = 0, (0, 7) if so, find the equations of lines…

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Q: The families of curves represented by the solution of the equation dy dx for n = - 1 and n = + 1,…

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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: Q2:Is the point lies on the curve? x* cos y- sin y= 0, (0, 7) if so, find the equations of lines…

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Q: 2 The diagram shows a sketch of the curve y = a sin(hx) + c , for 0 SIST. Find the value of a, b and…

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Q: Consider the following. a) Verify that the given point (7,7) lies on the curve. x3 + y3 = 14xy b)…

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Q: 13. Consider the curve given by the equation cos(x) + xy? = 5ey - 5. dy (i) Find dr (ii) Find the…

A: Given

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=&lt;t+1,t,1t&gt;=&lt;x, y,…

Q: Consider the following. X = 7 cos(0), y = 8 sin(0), - T/2 < 0 S TT/2 (a) Eliminate the parameter to…

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Q: 1. a) Find the equation of the tangent line to the curve given by F(t) = (cos(nt), t, 1 + t2), for t…

A: First we find r(2) and r'(2). Then find equation of tangent line to given curve r(t).

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: 3. Which of the following is the equation of the tangent () line to the polar curver = sec at the…

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Q: Find T, Ñ and B for the curve 7(t) = (2 cos(4t), 2 sin(4t), 5t) at the point t = 0 Give your answers…

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Q: Find T, Ñ and B for the curve 7 (t) = (3 cos(3t), 3 sin(3t), 5t) at the point t = 0 Give your…

A: Space Curves and T, N, B vectors The unit tangent vector T, the unit normal vector N and the unit…

Q: 2. A curve C with equation y = sin2x 0 < x <5, has a stationary point, P. e3x dy (a) Find an…

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Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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Q: Q.2. (3 points) Find the exact length of the curve y In(cos x),0 < x <

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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: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: (a) The curve with equation y? = x3 + 3x2 is called the Tschirnhausen cubic. Find an equation of the…

A: To determine the equation of tangent line.

Q: Find the cartesian equation of the curve

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Q: The curve with equation y= e* In(x- 1) has a stationary point when x = p. (i) Show that p satisfies…

A: Given- The curve with equation y = e-2x lnx - 1 has a stationary point when x = p. To Show- Show…

Q: Q2: Find parametric equations of the line tangent to the graph of r(1) at the point where t= to.…

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Q: Q2:Is the point lies on the curve? x² cos² y – sin y = 0, (0, ) if so, find the equations of lines…

A: given curve is                                                  x2cos2y-siny=0,   (0, π) we have to…

Q: The x- coordinate of the point on the graph of y = yx – 1 at which the tangent line is perpendicular…

A: Topic- application of derivatives

Q: 25. Consider the curve defined by the equation below and a point (2, 1) on the curve. What is the…

A: topic - equation of a tangent line