[x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

Q: Find the equation of the tangent line to the curve defined by the parametric equations x(t) = 2t3 -…

A: Topic- application of derivatives and tangent equation

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

Q: (a) Find the slope of the tangent line to the parametric curve x = t/2, y = t 2 + 1 at t= −1and at t…

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Q: Find parametric equations for the line tangent to the helix

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Q: Find the equation of the line tangent to the parametric curve 2t r(t) %3D t2 +1 - 0 <t<0 12 -1 y(t)…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

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

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

A: Given parametric equations of a curve.

Q: Consider the parametric equations x(t) = 1 + 3t2, y(t) = 4 + 21³, -1 <t <1. • What is the length of…

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Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Given:

Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

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: Consider the smooth parametric curve defined by the equations = t (t² − 3) = 3 (t² − 3)' X Y where…

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Q: Find parametric equations for the line that is tangent to the curve r(t) = e^t i + (sin t)j + ln (1…

A: The given curve is Differentiating with respect to t, we get Now, we find r(0) and r'(0) and

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

A: x=8 cos (t) y=2 sin (t)

Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…

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Q: Consider the parametric equations defined by x(t) = 3t² – 3 and y(t)= 2t +1, for t> 0. d'y at t= 1.…

A: Option A is correct option.

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

Q: Find the points on the parametric curve c(t) = (3t 2 − 2t,t 3 − 6t)where the tangent line has slope…

A: This question is taken from the tangent and normal in which we have to find points on the given…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: Find parametric equations of the line tangent to the graph r(t) = (t cos 7t)i - (t+ t)j+ sin(t)k at…

A: Given that rt=t+cos 7ti-t2+tj+sintk   Tangents to the curve is given by Tt=ddtrt Tt=ddtt+cos…

Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: Find the dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: Consider the curve described by the parametric equations ¤ = t² +4 and y = 3t + 4t. Determine the…

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Q: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

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Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: B) Find parametric equations for the line that is tangent to the curve r(t) = e'i + (sin t)j + In(1…

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Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Find the derivative of the following parametric equations. (a) x = t2 + 5t + 4, y = 4t (b) x = 0 –…

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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: Consider the parametric curve C: x=t³ + 1, y = t² – t,0 <t < 3. Find the equation of the tangent(s)…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: Answer

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: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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Q: 2. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

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Q: 2. * (t) = t lnt and Y (t) = (t – 1)?

A: We need to find the first and second order derivative of the given function. This can be done as…

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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

A: The tangent line to the curve in parametric form is given as follows

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative

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

Q: Consider the smooth parametric curve defined by the equations t (t²-3) { = = 3 (t² - 3)' = where t E…

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Q: Consider the following parametric equations: x=t^2+5t+4, y=4t. Find dy/dx, d2y/dx2, and the line…

A: Please refer to the image below

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.