Describe a circle of radius a centered at the origin, x² + y? = a², using parametric equations. Then (出) dy dy use the formula dx dt to find the slope of dx dt the tangent line to the circle at the point (x, y). dy Be sure to convert your representation of dx from being in terms of t to being in terms of x and y.

Q: The function y=f(x) is given in parametric form by the equationsx=t+cost,y=1+sint,where t∈(0,2π).…

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Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

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Q: differenetiate parametrically to find dy/dx in terms of t:  x=1/t+1 , y=2t^2-4

A: please use according to form i did solved two equation because your question is not write clear that…

Q: X = cost y = tant – 3 t = T/4 on the curve given by the parametric equation is the ordinate of the…

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Q: Find dy/dx of the following set of parametric equations 1. x = 3(t-2)2 ,  y = 9t2 + 4 2. x =…

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Q: Find a/dx? at t=1 by the given parametric equations. *=t2 and y=t³. d²y/dx² is! 2 is Blank 1. The…

A: Use double differentiation

Q: Find dy/dx and d'y/dx", and find the slope and concavity (If possible) at the given Parametric…

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Q: Given the parametric equation x = t+ lnt and y = t - Int %3D dy d²y Find and dx da? Find the point C…

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Q: de termine d3y f the parametric equatio ns. of dx2 x (t) = tlht and ylt) = (t-1)-

A: This question is based on diffrentiation of parametric curves.

Q: dy Using the parametric differentiation find dx if x = 9e%, y = 4e18t 0.44 e9t 8.11 et 0.89 e9t 1.33…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find dy dx2 Q2 when t = 1 if given the parametric functions as below, x = 3e5t y = te-5t

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Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t.

A: As we know that; The Power Law: ddxxn=nxn-1 The Product Rule: f·g'=f'·g+f·g' The Chain Rule:…

Q: A curve is defined by the parametric equations x (t) = at² and d² y y (t) = bt where a and b are…

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Q: Find dx for the parametric curve c(t) (31°, 312 – 7) at the point t = 4. %3D (Use symbolic notation…

A: Given: Parametric curve ct=3t3,3t2-7 Parametric curve c(t) is represented as c(t)=(y(t),x(t)) So,…

Q: Find the parametric equation for the line tangent to the r(t)=sinti+(t2-cost)j+etk curve t=0 at the…

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Q: dy 14ya® dx such that y(0) = 6. y(x) =

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Q: Given the parametric curve and value of t x(t) = Vf, y(t) = 2t + 4 dy at t = 4 dx Find dy help…

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Q: A curve is defined by the parametric equations x (t) = e¬t and y (t) = e3t. What is d'y in terms of…

A: The solution for the above problem is shown below.

Q: What is the formula for the derivative for dy/dx for a polar curve r=f(theta)?

A: Given that

Q: Find dy/dx and d²y/dx², and find the slope and concavity (if possible) at the given value of the…

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Q: Find f d'y Find for the curve given by the parametric equations and determine the concavity dx?…

A: Given:X=t2Y=t3-5tTo fondAt t=1d2ydx2 and value of t for concavity

Q: Find dy/dx and d'y/dx, and find the slope and concavity (if possible) at the given value of the…

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Q: Use polar coordinate to evaluate (x² + y* )² dx dy . Leave your answer correct to two decimal…

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Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Find dy/dx and dy/dx2, and find the slope and concavity (if possible) at the given value of the…

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Q: Find dy/dx and d'y/dx², and find the slope and concavity (if possible) at the given value of the…

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Q: tind the area of the parametric curve X = t ,4=9t-73

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Q: dy (ii) Find dx? for the parametric equations x = t+ sin t, y= 1+cost

A: • This problem can be solved by using Chain rule as explained in step 2.

Q: Differentiate parametrically to find X 1 t-1 y=t³+2 dy dx in terms of t:

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Q: d/dx(y(x)) if x and y are related by the parametric equations x = t+sint, y = t^t

A: Given  equations x = t+sint, y = t^t

Q: (ь) Find the value of a for which the tangent to the parametric curve = 4t° +t? + at, y = t – 6 at t…

A: Given the two parametric curves x=4t3+t2+αt   and y=t4-6. We need to  find the value of α for which…

Q: Find dy/dx and d'y/dx2, and find the slope and concavity (if possible) at the Parametric Equations =…

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Q: x = t? + 2t, y = 2' – 2t y. (15, 2)

A: Consider the parametric curve  x=t2+2t,                 y=2t−2t

Q: dy in terms of t: Differentiate parametrically to find dx 1 y = +2 t+1

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Q: dy in terms of t: Differentiate parametrically to find dx x = 4t2,y = 2t3 None of the other answers

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Q: Let C1 be the curve with parametric equations x = cost, y = sint – t, where t e [0, 5]. (a) Find the…

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Q: dy for the parametric curve x= 2e', y= sin(1 + e' ) dx Find

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Q: Find dy/dx and d?y/dx2, and find the slope and concavity (if possible) at the given value of the…

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Q: dy dy Find dx 1 and for the parametric curve x = y = dr? NOTE: Enter the exact answers. dy dx It=2…

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Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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Q: Find an equation of the tangent line of the parametric curve, I = 1+÷, y=t³ –t² +3,

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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: dy Find and dx d²y given the parametric equations: x = 2 – t and y = -1+5t2. dæ?

A: y=-1+5t2 dydt=ddt-1+5t2 dydt=-ddt1+ddt5t2 dydt=-0+10t dydt=10t take the second derivative…

Q: A curve is given by parametric equations x = t – 2 cost and y = t+2 sin t. dy and d?y in terms of t.…

A: The given parametric equations  x = t - 2cost ..... (1) y = t + 2sint......(2) To find  dydx,d2ydx2

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: A curve is given by parametric equations x = cos't and y= sin' t . dy d²y Find and in terms of t. dx…

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

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative