1. Given the parametric curve x = 3t2 – 1, y = 2t³ + 1. (a) Find the equation of the tangent to the curve that passes through the point (2,3) (in point-slope form). (b) Find the area under the curve for t E [0, 2]. (c) Find tbe length of the curve for t s (0 A1

Q: Find the exact value of 0.049768 x³y²z ds, where C is the curve with parametric equations x = e¯t…

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Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

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: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

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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: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

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: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

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Q: 2. For the parametric curve defined by: x(t) = t2 + 4t + 2 y(t) = t³ + 2t2 + 4t + 1 (a) determine…

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

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

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

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Q: A curve C has parametric equations 1 x = t t+±1. 1-t² dy in terms of t. dx (i) Find (ii) Show that…

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Q: (a) Find the slope of the tangent line to the parametric curve x = t² + 1, y = t/2at t = −1and t = 1…

A: Given,                          x=t2+1,   y=t2,    and               t=-1,            t=1

Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

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

A: The tangent line to a parametric curve given by c(t)=&lt; x(t) , y(t) , z(t) &gt; at some point…

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 10 cos(0) + 3 sin? (0) and…

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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: 1. Given: parametric curve H defined by r(t) = tan-¹ t and y(t) = e¹, where t € R (a) Find the slope…

A: Solved below.

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

A: The given parametric equation is: x=5 ln t  ,   y=4t   ,      z=t3 Given point is:  (0, 4, 1) From…

Q: 1. Find the equation of the tangent line to the curve: x = Vt, y = e² at t=1. d?y at t=1 for the…

A: Solve by using differentiation.

Q: 2 cos(t) T at the point 4 Find the slope of the tangent line to the parametric curve ly = 1 sin(t)

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

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

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

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Q: Given the parametric curve x = t – sin(t),y = 1 - cos (t), find an equation for the line tangent to…

A: Given: x=t-sint y=1-cost at t=pi/3

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

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

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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: 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: 1 A curve C is defined by the parametric equations x = and y = for 1z 0. VI +1 t + 1 dy (a) Find dx…

A: First find slopes then us equation of tangent line

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

A: Answer

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: 1 cos(t) ly = 3 sin(t) Find the slope of the tangent line to the parametric curve at the point

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

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Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

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

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Q: 13. Consider the curve C given by the parametric equations x=2–3cos t and y = 3+2 sin t, for –sis 2…

A: Formula a) dy/dx b) y-y1 = (dy/dx)(x-x1)

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

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