Question 19 Express the following parametrized curve by an algebraic equation in terms of x and y: x (t) = e' and y(t) = 6 – e2t a) O a2 -y = 6, x > 1 b) Oy - a2 = 6, x > 6 2² + y = 6, d) O y? + a = 6, > 0 * – y? = 6, x > 6 f) O None of the above. ()

Q: Consider the parametric equations y = e' +t te [1, 10] Briefly explain how you know that the curve…

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

A: Explanation :  Given that x= 3cost + sint y = e^2t

Q: Question 4 Evaluate fVdr which V given by V = xy + 2xy + yz between A(0,0,0) and B(2,1,3) along the…

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

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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: 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: 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: Suppose parametric equations for the line segment between (5, 3) and (3, – 8) have the form: S¤(t) =…

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Q: Suppose a parametric equations for the line segment between (5,2) and (7,8) have the form:  x(t)=…

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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: 5. Find the equation of the tangent line to the curve given by the parametric equations x(t)= 3r² –…

A: We are authorized to solve only 1 question, please repost remaining questions Equation of tangent to…

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: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…

A: Given: The parametric equation of the curve C is  x=tet, y=t+cost (a) To find: The equation of…

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10…

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,

Q: A curve passes through point leio) and the Sloge dt line of each point (^,y) is egual to xe-BY .In…

A: Curve passes through (e6, 0)f(e6)=0slope of Normal line=x e-8ySlope of normal line*slope of tangent…

Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: Suppose parametric equations for the line segment between (2, a(t) 6) and (0, 0) have the form: = a…

A: Explanation of the solution is given below...

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: Let C be the curve.

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

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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: 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: Suppose parametric equations for the line segment between (6, 7) and (4, 5) have the form: Sa(t) = a…

A: The parametric equations for the line segment between (6,7) and (4,5) have the…

Q: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

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Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

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Q: Suppose a curve is traced by the parametric equations x = 2( sin(t) + cos(t1) %3D y = 23 – 6 cos (t)…

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Q: Suppose parametric equations for the line segment between (8, – 3) and (9, 2) have the form: S¤(t) =…

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Q: (11) Find the tangent line(s) to the parametric curve given by * = t5 - 4t3 y = t2 at (0, 4)

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Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: Question 12 Find a at time t = 1 for the plane curve r(t) = 4t²i+ 3tj. Round your answer to three…

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Q: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

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Q: Suppose parametric equations for the line segment between (6, – 9) and ( – 1, – 5) have the form:…

A: ...............when  ...............when  .

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. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

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Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1 + √t, y = e^(t^2)…

A: Given parametric equation of curve x=1+t   y=et2we want to find equation of tangent at  ( 2, e)

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: 11. C is the curve F(t) = ( In (2 Vt +3 Find parametric equations for the tangent line to C at the…

A: Note: Here, the given point (0,1,2) is incorrect there should be(0,-1,2) because the point is on the…

Q: A parametric curve has the equations x =t+sin t and y= cos t. Calculate and , both evaluated at t=…

A: Use dy/dx= (dy/dt)/(dx/dt)

Q: A curve is described parametrically as x = e' sint, y = e'cost, – o <t< ao. Find the equation of the…

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Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the…

A: We have the given parametric curve t,t2, t∈0,1x=ty=t2 for t∈0,1the first order derivative the curve…

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: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

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Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…

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

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Q: Suppose parametric equations for the line segment between (6, 1) and (7, 7) have the form: Sx(t) = a…

A: We have find four unknowns so we need four independent equations.

Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem