The given curve is rotated y = 3 - x2,

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

Q: Find the length of the curve y = xVa 0 <x < 1.

A:

Q: The curve ver = V1 + sin20.

A: Solution :-

Q: 5. Trace the curve r = sinocos³o.

A: Given curve: r=12sinθ cos3θ

Q: Find the points on the curve xy2 = 54 nearest the origin.

A:

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

A:

Q: Consider the following. x = et - 4, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A: To find The cartesian equation of the curve by eliminating the parameter

Q: Find the exact length of the curve.

A:

Q: Find T,N and k for the curve:

A:

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

A:

Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: Consider the following. x = et − 4,    y = e2t   Eliminate the parameter to find a Cartesian…

A:

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = 4t2, y = t3 - 1

A: We have given curves; y = ƒ(x) . x = 4t2, y = t3 - 1

Q: the sloper of the curve 2y = ax? +b at (1,–1) is – 1.Find a, b

A: We have given the sloper of a curve at (1, -1) is -1 .  We have to find the value of a and b.

Q: / Fit a curve of the form y = ax + bx² to the data

A: Given,    x 1 2 3 4 5 y 1.8 5.1 8.9 14.1 19.8 To find             y=ax+bx2…

Q: The graph, when the curve y=v(3+ x^2 ) from x = 0 to x = 4 is rotated about x - axis is ....

A: This question can be solved using the concept of volume of solid generated when curve is rotated…

Q: Find the points on the curve 5x + 5y? - 6xy - 6xy = 4 nearest to the origin.

A:

Q: Find the exact length af te of the curve, 2. x-

A:

Q: Find the points on the curve y = 14x closest to the point (0, 1). and

A: This question is based on application of Derivative.

Q: Find the length of the arc of the curve in the given range, x3 + 3 1 у %3D25х + 5x2 + 0 <x< 5 4(x +…

A: The arc length of the curve is given by integral:

Q: Find the exact length of the portion of the curve shown in b r = 0+ 2 2 (i)

A:

Q: If a curve C is given by r(t) = ⟨t, t2⟩ , what is | r'(t) | ?

A:

Q: A curve is defined by the equation xy - 6+x?y = 0. (a) Verify that the curve passes through the…

A:

Q: y =(+ + +)* x = 4t + 1, 4

A:

Q: Find an equation of the curve that satisfies dy 20ya de and whose y-intercept is 3.

A:

Q: Find the length of the arc of the curve in the given range, x3 + 3' 4(x + 5) ' 1 y = 25x + 5x²+…

A:

Q: Find the orthogonal trajectory of the given family of curves. y=c*e^(2x)

A:

Q: The family of curves orthogonal to x2 + 4y2 = c2 has the general equation 04. %3D

A:

Q: a) Given a curve y = px* + 2x has turning point at (–1,q). Find the value of p and q.

A:

Q: The graph, when the curve y = √3 + x² from x = 0 to x = 4 is rotated about x - axis is A B C D

A: To find the graph of the solid formed by rotating the given curve about x axis, first we find the…

Q: Use the guidelines of this section to sketch the curve.

A:

Q: Find the 0lar eauatiDo for the curve represented by the given Cartesian euation.

A:

Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: Trace the curve r = sinocos'o. 2)

A: Given: r=12sin3θcos3θ Explanation: r=12sinθcos3θat θ=0r=12sin0cos30=0⇒r=0at…

Q: 6x 4. У3 y = х+3

A:

Q: Eliminate the parameter t to find a Cartesian equation of a curve. x = 1 + 3t,  y = 2-t^2

A:

Q: Find the length of the arc of the curve in the given range, y3 +. 3 1 x = 16y + 4y² + 0 < y< 4…

A:

Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Find the length of the arc of the curve in the given range, x = 16y + 4y2 + ン3 +. 3 4(y + 4) 0 < y<…

A: In the question we have to find length of Arc of the curve.

Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

A:

Q: Sketch the curve with equation  x2/3 + y2/3 = 1  and use symmetry to find its length.

A:

Q: Find the orthogonal trajectory of the given family of curves: 1. y = C(sec x + tan x)

A:

Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

A:

Q: Find the exac length of the curve 3/2 , 0dxE y=2+2x

A:

Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 5< xs 6,

A:

Q: Find the exact length of the curve. y = In(sec x), 0s x s a/3

A: This question is based on application of Derivative.

Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem

Q: Question 5 Find the length of the curve. +- from y = 1 to y = 2 %3D 4y2 2

A: