The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

Q: a) Plot the parametric curve x=1 – sin t, y=1+ cos t with 0 <t< ™. b) Determine the equation of the…

A: Given: For the curve x=1-sin(t) t 0 π/2 π x 1 0 1

Q: Find the tangent line to the Curve t) =(sin 4), cos (t),+> at (0,l,0) क

A: We are given parameteric equation of curve .

Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t). dz 4cos4t…

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Q: The parametric form of the tangent line to the image of f(t) = (2t², ?,t +2) at t = 1 is L(t) =

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Q: ind the equation for the tangent lin to y- fcx) at the specified point. fcx) where x=1 x2

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

A: A detailed solution is given below.

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: Find the equation of the tangent line to the parametric curve at (1, 3). z =1+ Int y = t +2

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Q: Find the equation of the tangent line to the curve given by F(t) = (cos(rt), t, 1+ t²), for t € [0,…

A: (a) First find the derivative of the given curve.  r't=-πsinπt, 1,…

Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

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Q: The parametric form of the tangent line to the image of f(t) = (4t2, ,t+ 4) at t = 1is L(t) =

A: First we will find the tangent vector by differentiating f

Q: Find the tangent plane to the equation 3y cos(4x – 2y) at the point (2,4,12) Z =

A: Z=3ycos(4x-2y)  Point= (2,4,12)

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Find the implicit equation of the tangent plane to z = In(x² + 1) + y² at the point (0, 4, 16).

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Q: Find the tangent plane to the equation 5y cos(2x – 4y) at the point (4, 2, 10). - = Z z =

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Q: Find the equation of the tangent line to the curve given by y. Sin (z) + e² - Tan (y – 1) = 0 a the…

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Q: Find the derivative of the parametrically defined curve (t) = 2 cos(4t), y(t) = sin(4t).

A: We have to find dy/dx.

Q: (a) x = 2 – T Cos t, y = 2t – T sin t -

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Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

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Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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Q: Find the tangent line equation to the parametric curve x = cos t y = sin³ t at t = V2 O A. y = -x +…

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Q: Find the equation of the tangent plane to z = In(x²y) – x/y at (-;4).

A: Let x0,y0 be any point of surface function z=fx,y. Then the surface has a non vertical plane at…

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: f(x,y) = 4x² + y² + 2 at the point wherex = 1 and y = 1.

A: The equation of the tangent at point (1,1) is: z=f(1,1)+fx(1,1)(x-1)+fy(1,1)(y-1)

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

Q: Find the equation of the tangent plane to z = ln(x³ + 1) + y³ at the point (0,6,216).

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find the equation of the tangent line to the curve at the point (-÷5) (글 given a cos(2 y) = 0. V3 a)…

A: We need to find the equation of the line.

Q: The slope of the tangent line to the curve parametrized by the equations x (t) = -2(cos(t) + t…

A: Slope of tangent is equal to dy/dx.

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: The equation of the tangent line to the graph of VT is given by y = mx + b for y = tan(4x) at x = т…

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Q: 2- Find the equation of the tangents to curve given parametrically by Y= sin(x²) + 1 at (x,y)= (…

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Q: Find the equation of the tangent plane to z = In(x³ + 1) + yª at the point (0,3, 81).

A: We have to find equation of tangent plane at (0,3,81).

Q: Find parametric equations for the tangent line to the curve given by x=ln(t+1), y=tcos2t, z=et at…

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Q: x² = y + 3y.

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Q: Find the exact length of the curve. y = In(cos(x)), TC 0 < x<.

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Q: Find an equation for the tangent line to the curve parametrized by x = e³t sin(πt) and y = et at the…

A: x=e3tsin πty=e2t

Q: Find the equation for the tangent plane to the graph of h (x, y) = y sin (x y) + yª + 3 x² at the…

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Q: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: The parametric form of the tangent line to the image of f(t) = (3t2,,t – 2) at t = 2 is L(t) =

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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: s Find the exact slope of the tangent line to the parametric curve π t = x = 9 cos(t) y = 4 sin(t)…

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Q: Find the tangent line equation to the parametric curve cos t y = sin t at t = O A. y = x+ O B. y =…

A: If the parametric equations of a curve are given variable t, then the slope of the tangent is the…

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: Find an (1,1) equation of the tangent i ine at the curue yt+xy = x_x+a. on

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Q: Find the equation of the tangent line to the graph of f(x) = 5 sin(x) + 6 cos(x) at x = equation: in…

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Q: VI. x = v1 - t , y = t³ – 3t

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