12. (8 points) Let C be the parametric curve determined by x = 4t? – 1 y = t2 – 2t where t is a real parameter. (a) Determine the x and y coordinates of the point when t = 2. dy (b) Determine dx |t=2 (c) Find an equation for the line tangent to the curve C at the point where t = 2.

Q: 5. The curve C has parametric equations = (In t)? – Int, y = In t2 - t2, (1) Find the exact…

A:

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

A:

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

A:

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

A:

Q: 18. The parametric equations of a curve are given by x= at", y= 2at, where a is a constant and t a…

A: To find the equation of tangent line

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A: Given, x=t^2-1 y=t^3+1 z=t^2 point (x1,y1,z1)= (8,28,9)

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: 4. Find the length of the curve having a parametric equation of x = a cos 3 6, y = a sin 2 0 from e…

A:

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

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Q: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

A:

Q: Find the parametric equations for the tangent line to the curve æ = t3 – 1,y = to +1, z = t° at the…

A: Find the tangent vector r't:                 r(t)=(t3-1)i +(t5+1)j +t5k Differentiate r(t):…

Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

A:

Q: 15) (10.) Sketch the parametric curve x = 2 + 3sin(t), y = -3+ 3cos(t) for <t<. Find the slope of…

A:

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

A: Given:

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

A:

Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

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: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0sts2M. 3.1. Find an equation…

A:

Q: curve has the following parametric equations with parameter t. x=2t-1/2t and y=2t+1/2t. Find dy/dx…

A:

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

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

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: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

A: The vector equation of the tangent line of the parametric curve r→t at point P is expressed by…

Q: 2. (a) Recall that or a parametric curve x = = f(t), y = g(t), where f, g are continuously…

A: Given: Q1 (a), x=t3+t, y=13t+2,  t∈R x=ft, y=gtht=dydx=g'tf't d2ydx2=dzdx, where z=ht To find: Using…

Q: 1. Find the equation of the tangent line to the curve x = e', y = et att = 1. 2. Find all values of…

A: tangent property

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

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

Q: Find the parametric equations for the tangent line to the curve x =t* _ 1,y=t* +1,z=t* - at the…

A:

Q: Find the First and Second derivatives of y with respect to x from parametric equations. a). x=3 (t…

A: x = 3 t + 22   and y = 9 t2 - 5⇒dxdt = 3 ×2 ×( t + 2)  , dydt = 18 t        Hence dydx = 18 t 6 ( t…

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

A:

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

A: Here we have to find the parametric equations for the tangent line to the curve with the given…

Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

A:

Q: 5. Determine the slope of the tangent line, the the equation of the tangent line, and the concavity…

A: this is the equation of tangent line.

Q: 3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

A:

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

A:

Q: 8. The tangent line to the curve r(t) = Li+ej=t'k 2-t at the point P(1,1, -1) intersects the line…

A:

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

A:

Q: where t € [0, 1]. x = cost, y = sint-t,

A: Here we will find the equation of tangent and length of curve P,

Q: Find the equation for the line tangent to the parametric curve: t3 – 9t - 9t2 – t4 at the points…

A:

Q: Determine the (1) graph, (2) initial and terminal points, (3) orientation, (4) the dy derivative and…

A: x(t)=3+sin(t), y(t)=-2+cos(t)   where π≤t≤2π   Graph

Q: 5. Sketch the parametric curve x = t2 – t, y = t³ – 3t and determine the location (x, y and t) where…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

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

A:

Q: Find the parametric equations for the tangent line to the curve x=t^4−1, y=t^3+1, z=t^2 at the point…

A: Consider the given curves and points.

Q: 5. Given the parametric curve x=r - 31 + 2, y=t-r a) Find the equation of the tangent line at the…

A: In this question we will use basic of calculus i.e application of differentiation. We will use the…

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…

A: We find parametric equations for the tangent line to the curve with the given parametric equations…

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

A: Let's find.

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

A:

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)