Q2:Is the point lies on the curve? x² cos y- sin y = 0, (0, 7) il so, Gind the equations of lines that ure (a) tangent and (b) normal to the curve at the given point.

Q: Consider the parametric curve defined by x = t – 7, y = t* + 13t. What is %3D - the slope of the…

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Q: 4. Sketch the graph of the curve y = Vx and the tangent line in the Cartesian Plane using a scale of…

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Q: Which of the following is the equation of tangent line of the curve that is given 2t by parametric…

A: As two Questions are given , I will solve the first one :We are given  the parametric Equations :…

Q: I the slope of the tangent line to the parametric curve X = 3 cos (t) y = 2 sin(t) ㅠ R 4 at the…

A: Given query is to find the slope of the tangent.

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: 5. Find the length of the curve given by x = cos t +t sin t, y = sin t – t cost, -T <t <

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Q: (a) Find the slope of the tangent line to the parametric curve x = 3cos t, y = 4sin t at t =…

A: Given, x=3cost,y=4sint at t=π4 and t=7π4. Differentiate the functions x and y with respect to t.…

Q: Let r(t)= be the position function for a particle at time t. b)When is the particle’s speed at a…

A: Solve the question as solved below.

Q: :2 cos(t) y = 3 sin(t) T = Find the slope of the tangent line to the parametric curve at the point 4

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: Find T and N for the curve 7(t) = (3 cos(5t), 3 sin(5t), 2t) at the point t = 0 COS Give your…

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Q: a) Find the equation of tangent line of curve that is given by parametric equations X = 3cost + sint…

A: (a) Given  parametric form of curve is…

Q: IL. Find the equations of the tangent and normal lines at the paint indicated. b. 4x - 4y - sin(x +…

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Q: A curve with equation y cosx %3D 0 <x < T, has a stationary point at Q. е 3x dy (a) Find an…

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Q: x = 2 cos(t) Find the exact slope of the tangent line to the parametric curve at the point where y =…

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Q: Tangent are drown from the origin to the curve y = sin x.Prove that their points of contact lies on…

A: Consider the curve y=sinx Here, the objective is to prove that the point of contact of tangent from…

Q: Consider the curve where a is the last digit of your exam number. (a) Compute=7 (t) at t € [0, +∞).…

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Q: 2. Find the length of the curve 1<t<4. given by r= e'(sin t+cos t), y = e'(cos t-sin t), OS

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Q: Consider the curve f(x)= sinx - cosx + 1 i) find f'(x) ii) Hence or otherwise, find the maximum…

A: f'(x)=differentiates f(x) w.r.t x

Q: = = 2 cos (t) lu =1 sin(t) T Find the slope of the tangent line to the parametric curve at the point…

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Q: Determine the equation of the tangent line to the given path at the specified value of t. (Enter…

A: Given that, r(t)→=[sin(7t), cos(7t), 2t9/2] We have to find equation of tangant line at t = 1.

Q: A curve C has parametric equations x = e' , y =t- Int, where t>0. (i) Show that there is no tangent…

A: Answer

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: Determine the equation of the tangent line to the given path at the specified value of t. (Enter…

A: Given:Determine the equation of the tangent line to the given path at the specified value of t.

Q: Q: Find the condition that the line x cos a +y sin a = p may touch the curve x"y" = a™*".

A: Answer

Q: x = 1 cos(t) y = 2 sin(t) Find the slope of the tangent line to the parametric curve at the point

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Q: Find an equation of the plane tangent to the following surface at the given point. 13 cos (xyz) =- 2…

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Q: V. The tangent line at the point (t, y) = (- to 4'2 1 Then, the curve y = cos t is y = bt - - - a a…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Given the curve r(t)=(4t2)i+(3t+1)j+(t3)k. We need to find parametric equations for the line that is…

Q: length of the parametric curve defined by x = t³ +2, y = 2tº/2, for 1 <t < 3. e the arc

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Q: . Find the parametric equations for the tangent line to the Curve at the Specific point. X = e-t cos…

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Q: x = 2 cos(t) Find the slope of the tangent line to the parametric curve at the point y = 3 sin(t)…

A: The derivative dydx defines the slope of the tangent drawn to the curve.

Q: Consider the parametric curve x = sint + cos t, = cos² t 0 <t < 2n п Find an equation for the…

A: We find dx/dt and dy/dt from the given equations

Q: A cycloid has parametric equations z =t - sint, y = 1 - cost, 0 <t< 2x. Find the slope of the…

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Q: i Find the eguation iof the tangent line to Uthe curve y sin 2x =X COS24 at Hohe point (T7/2,…

A: Explanation of the answer is as follows

Q: Find an equation of the tangent line to the curve y = 4x sin (a) at the point (T /2,27). Express…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

A: Consider, r(t)=lnt4i+t-4t+8j+t lnt4kWe first evaluate r(t) at t=t0=4r(4)=ln44i+4-44+8j+4 ln44k…

Q: The tangent to the curve x? – xy + 2y? – 4x + 2y +2 = 0 that is parallel to the line x– 4y = 2. The…

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Q: (* = 8 cos(t) y = 7 sin(t) Find the exact slope of the tangent line to the parametric curve at the…

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Q: {; 4 cos(t) 2 sin(t) at the point 4 Find the slope of the tangent line to the parametric curve

A: We have the parametric equation of curve as x=4cost⇒cost=x4        ⋯⋯1y=2sint⇒sint=y2          ⋯⋯2…

Q: Q4) Show that the point (-1, 0) lies on the curve 6x2 + 3xy + 2y2 + 17y - 6 = 0. Then find the…

A: Substitute x=-1 and y=0 in the given equation Then 6(-1)2+3(-1)(0)+2(0)2+17(0)-6=0

Q: 5. Given the parametric curve x=r - 31 + 2, y=t-r a) Find the equation of the tangent line at the…

A: In this question we will use basic of calculus i.e application of differentiation. We will use the…

Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: 4 cos(t) { Find the slope of the tangent line to the parametric curve at the point 1 sin(t) 6 Y =

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Q: Find any points on the curve given by x = t + sin t, y = cos^2(t), 0 ≤ t < 2π where the tangent is…

A: Here, the given curve is: x=t+sin t, y=cos2t, 0≤t≤2π To find the points where the tangent is…

Q: Show that the curve x = 3 cos(t), y = 2 sin(t) cos(t) has two tangents at (0, 0) and find their…

A: on solving this we get

Q: B The equation of a curve is y = cotx - 8 cos x, 0<x< π, find the coordinates of the points on the…

A: If the equation of the curve is given y=f(x)  Then we find dy/dx and then equating to 0 we get the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.