A. Find the derivative of the following parametric equations as indicated. Express the final answer in its simplest form without negative exponents. sr=(u- 3)³ ,y = (u + 3)², y"

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Explanation :  Given that x= 3cost + sint y = e^2t

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 the Cartesian equation of the curve: [2r/r2 = 1+ cos a]

A:

Q: Find an equation in rectangular coordinates for the curve r^2 = cos 2θ.

A: We know that, the relationship between polar and rectangular co-ordinates are given as r2=x2+y2…

Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent to a curve at a point is a line that just touches the curve at that point and in some sense…

Q: Find a parametric equation of the line tangent to 7 (t) at the point (– 12, 144, – 4.159)

A:

Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

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

A: The equation of a line can be obtained by using the expression y-y1=m(x-x1). Here, m is the slope of…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: It is given that, x=3cost+sinty=e2t  Slope of tangent is defined as, m=dydx(x,y) While general…

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

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

Q: Find parametric equations for the given curve. y = 4x2 - x

A: The given curve is y = 4x2 - x

Q: Find the parametric equation of the line through a = 3 A co which is parallel to b = 2

A:

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: ELIMINATE THE PARAMETER IN THE PARAMETRIC EQUATIONS: x=t +1 Y = t t-1

A: Topic - equations

Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

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

A:

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: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: The curve defined by any parametric equations X = f(t), y = g(t) is always a function.

A:

Q: 3. Find the second derivative for the following set of parametric equations a. x = sqrt(t) , y = 2t…

A: We have to find te second derivative.

Q: Find the derivative of the following parametric equations as indicated. Express the final answer in…

A:

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: The equation of a tangent line passing through the point x1, y1 and slope m is y-y1=mx-x1. The slope…

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

A:

Q: Find the derivative of the following functions/parametric equations: 8. x = 3t – 5|y = t² – 6t + 4

A: Given:- x = 3t-5 y = t2 -6t+4 To find:- Derivative of given parametric equations

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Given: The parametric equation of a curve is x=3 cos t+2 sin t ,  y=e6t To find: The equation of the…

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=<t+1,t,1t>=<x, y,…

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

A:

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 a set of parametric equations that represents the graph of y = 1 − x2, using each of the…

A: Given- y=1-x2 To find- Find a set of parametric equations that represents the  above graph using…

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: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: Find the Cartesian equation of the parametric equations x = a cost y = b sint 0<t< and identify its…

A:

Q: Consider the parametric equations below. x = t?, y = t3 X =

A: Given data:     The first parametric equation is: x=t2. The second parametric equation is: y=t3.…

Q: express the parametric curve in the form y = f (x) c(t) = (4t − 3, 10 − t)

A:

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

A:

Q: Which one of the following equations is the equation of the tangent plane to the surface xy + xz +…

A:

Q: Find the slope of the line whose parametric equations are x=4t+6 and y=t-1

A:

Q: Find the equation of the tangent line(s) to the given set of parametric equations x = t² + 5t – 6 y…

A:

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

A:

Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

A:

Q: Find the equation of the tangent line to the curve described by the parametric equation described…

A: To find the equation of the tangent to the curve described by parametric equation x=t4+2y=t3+t3,-2

Q: Find parametric equations for the tangent line to the curve of intersection of the cylinders x2 +?…

A: Given      x2 + z2 = 25 and y2 + z2 = 25 at the point (3,-3,4) Let    f(x,y,z) = x2 + z2 - 25  and…

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: x = V1 - i , y = t³ – 3t

A: We have to find derivative

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

A: Let's find.