The curves x=y²and x = 2 y – y?

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

A:

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

A: Given data: First curve xy=3. Second curve x2=9y.

Q: Find the length of the curve :   x=(y^3/2)/3-y^1/2 from y=1 to y=9

A: The given curve is: x=13y32-y12        from  y=1  to  y=9

Q: Find the exact length of the curve. 4 1 X = 1<y< 3 + 8 4y2"

A: we will find the exact length of the curve.

Q: Find the curve length 3 y = 1+ 6x7,0 <x<1

A:

Q: Find the points on the curve x2 + xy + y2 = 16 which are nearest and farthest from the origin.

A: Given curve is g: x2+xy+y2=16 If x,y is any point on the curve g: x2+xy+y2=16 Then square of the…

Q: 1 Find the length of the curve x= from y 1 to y=2. +. 16y

A:

Q: The x coordinate of the point of intersection between the two curves y = el4a and y = 1 is

A: Equate both equation

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 a coordinate of the point of intersection between the two curves y = ellz and y= 1 is x =

A:

Q: The x coordinate of the point of intersection between the two curves Y = e2lx and y = 1 is

A:

Q: Sketch the ff curves: a) Y = x2 ex 1+lnx b) Y = c) Y= (x²–4)2

A: Given: a)y=x2e-xb)y=1+lnxxc)y=x2-42x-4

Q: Find the length of the curve x = y^4/16 +1/(2y^2) between y= -3 and y= -2.

A: we have to find the length of the curve . I have explained in details please see the explanation and…

Q: tind the point on the curve y=Jx that is closest to the point (3,0).

A:

Q: Describe the shape of the curve x = 3 cost,y = 3 sin t.

A: We have to describe the shape of the curve x=3cos(t) ,y=3sin(t)

Q: Find a point on the curve y = x² that is closest to the point (18, 0). %3D AY y =2 (x, y) (18, 0)

A: Find a point on the curve y=x2 that is closest to the point  Here use distance formula…

Q: Find the point on the curve y =√ x that is closest to thepoint (3 ,0) .

A: Let (x,y) be the point on the given curve which is closest to the point(3,0) where The distance…

Q: Find the point on the Curve y rx that is closest to the point (2,0)

A:

Q: Find the length of the curve x = 1+ 312, y = 4 + 213, 0 <t < 1. Length =

A: Given,

Q: b) Find the point on the curve y Vr that is closest to the point (7,0).

A: Find the point to the curve y=(x)^(1/2) that is closest to the point (7,0)

Q: The x coordinates of the points of intersection between the two curves y = I* and y =-I + 12z are

A: Given : y = x2y = -x2 + 12x

Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that…

Q: X = 8 1 + 1 < y< 2 4y2'

A: We find the length of the given curve by using the formula of length of the curve. The length of a…

Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

Q: dy Find for the curve x-2.x'y-20y 2 at point (-2,1). de

A:

Q: B. Find the length of the curve y= x2 from x = 0 to x = 7.

A:

Q: Find the point on the curve y = Vx +1 that is closest to the point (5,0)

A: We will use second derivative test to find the smallest distance among point (5,0) and curve

Q: Find the exact length of the curve. y = 4 =Dx2-을 In(x), 1sxs6 =

A:

Q: Find the exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Find the exact length of the curve. 1 + X = 8 , 1< y< 2 4y2'

A: It is given that,       x=y48+14y2,   1≤y≥2we have to find the exact length of the curve.   So, we…

Q: Find c so that the line y = 4x + 3 is tangent to the curve y= x^2 + c?

A:

Q: Find the length of the curve x = 3t2 + 10, y=2t3+ 11, O<t<1.

A: Given,         The length of the curve x=3t2+10 , y=2t3+11 , 0≤t≤1We know that,         The length…

Q: Find the angle between the curve 2y=e-x/2 and y-axis

A: we will see in next step

Q: Find the length of the curve 3x = (y² + 2)³/2 from y = 2 to y = 3 %3D

A: Use length of curve formula:-  for a given curve x = f(y) from y=y1 to y=y2 length of curve,…

Q: xy = -4 and y² = 2х

A:

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

A:

Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

A:

Q: Find the length of the curve y = 4 1 between x 1 to x 2. %3D &x2

A: It is length of curve.

Q: What is the length of the curve I=1+32, y = 4+2t, (0 <t<1) ?

A:

Q: Find the exact length of the curve. x = (2y + 1)3/2, 0<y<3

A: Differentiating with respect to y, we get

Q: For the curve y = ax3 + bx2 + 12x - 7, what values of a and b will make the tangents to the curve at…

A: We have to find the value of a and b according to the given information

Q: Find the length of the curve 3 y = x7 – 2 from x = 0 to X = 4.

A:

Q: s to the curve y = x* at the %3D

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: Find the length of the curve y = (x/2)2/3 from x = 0 to x = 2.

A:

Q: The x coordinate of the point of intersection between the two curves 12x y = = el2# and y = 1 is x =

A: Our Aim is to find the x coordinate of the points of intersectionbetween the two curves y=e12x and…

Q: Find the length of the curve. 33) y-승. from x = 1 to x= 5 2x

A:

Q: Find the exact length of the curve. Y=y4/8 + 1/4y2, 1 less than or equal to Y less than or equal 2.

A: Given: Y=y48+14y2 , 1≤y≤2 As, the length of the curve, L is given by: L=∫ab1+dydx2dx According to…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.