Find the points of intersection of the curves y = 5x2 - 3x - 2 and y = 2x - 1.

Q: Find the exact length of the curve.   y= 2/3x3⁄2,    0 ≤ x ≤ 4

A: Given query is to find the length of the curve for the interval.

Q: Find the length of the curve defined by Y = 3x³/2 + 3 from x :3 to x = 9.

A: Question: Find the length of the curve defined by y= 3x^3/2 + 3 From x=3 to x= 9

Q: Find the point of inflection of the curve y = x^3 - 6x^2 - x + 12. (-2,6) (2,-6) (-2,-6) (2,6)

A: We have to find point of inflection of given function.

Q: Find the point of inflection of the curve 6x – x' +5 y = 7 b. (2, 4) d. (3, 1) а. (0, 1) с. (2, 3)

A: Inflation point of a curve is a point on the curve at which concavity of the curve changes means it…

Q: Find the points of intersection of the line y = 5 x with the curve y = 3 x + x^2

A: In order to find the point of intersection of given line line and curve , we must find values where…

Q: Find the exact length of the curve. y = 3 + 6x³/2, 0≤x≤1

A: Given :y=3+6x3/20≤x≤1

Q: Explain the steps required to find the length of a curve y = ƒ1x2 between x = a and x = b.

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Q: Find the exact length of the curve. x = 9 + 6t2, y = 4 + 4t3,

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Q: Find the length of the curve y = x2, 0 ≤ x≤√3/2.

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Q: Describe the curve generated by x = 3 + 2t, y = -12 - 6t, for - ∞ < t < ∞.

A: Given: x=3+2t y=-12-6t            - ∞ < t < ∞ To find: curve generated by given functions.

Q: Find the exact length of the curve. y = 4 + 6x3/2, 0 < x < 1

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Q: find the slope of the curve at the point indicated y = 5x - 3x2, x = 1

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Q: Find the exact length of the curve. y=3+8x3/2, 0 less than or equal to X less than or equal to 1.

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

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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 line  y = 4x + 3  that is closest to the origin

A:

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0< x < 1

A: Given: y=fx=5+2x32, 0≤x≤1 we know that lengthL of curve in interval a,b is given by L=∫ab1+f'x2dx…

Q: What is the equation of a family of curves orthogonal to 2x2 + y2 = c?

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Q: Find the point on the line y = 3x + 4 that is closest to the origin.

A: Given, the line equation

Q: Find the length of the curve Y 12x', 1<X< 2

A: Given curve is: Y=X55+112X3, 1≤X≤2 To find the length of the curve.

Q: Find the exact length of the curve. y = 3 2x3/2, 0 < x < 6

A: We have to find length of curve

Q: Find a possible point of inflection of the curve y x +3x2 + 6x

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Q: Find the length of the curve X= -y², 1≤ y ≤9

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Q: Find the exact length of the curve.   y = 1+ 6x3/2 , 0 ≤ x ≤ 1

A: Find the exact length of the curve.

Q: Determine the length of the curve x = 3y2 -1 between y = 0 and y = 4 3/2

A: The given curve is x=3y32-1 We will find the arc length of the curve between y=0 and y=4

Q: Find the slope of the curve y = 2x* + 3x³ + 2x2 – 1 at a point where it crosses the x-axis

A: y=2x4+3x3+2x2-1 A curve crosses the x-axis at a point where its y-coordinate is zero. Therefore…

Q: Find the closest point to the point (2,0) on the y = x curve.

A: To find the closest point to the point (2,0) on curve y=x

Q: Find the length of the curve y=7x-13 between y=-6 and y=15.

A:

Q: find the slope of the curve x^2+y^2-6x-4y-21=0 at (0,7)

A: Given curve  x2+y2-6x-4y-21=0we find slope at (0,7)

Q: Find the length of the curve defined by y = 4x3/2 + 11 from x = 2 to x = 8.

A: We will differentiate the function and use the arc length formula.

Q: Find the slope of the curve defined by the equation x²y – 8 = 0 at the point (2, 2)?

A: The required slope of the given curve can be found as below

Q: Find the exact length of the curve.y = 1 + 4x3/2, 0 ≤ x ≤ 1

A: Given curve is

Q: Find the exact length of the curve. x3 y = 1 < x < 2 %3D 4x

A: y=x33+14x  ,  1≤x≤2.

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

A:

Q: / Find the length of the curve y = (÷) (x²

A: Given,         y=13x2+232

Q: Trace the curve: y^2 = 4x^2 / (x+5) (x-2)

A: We want to plot the graph ofy2=4x2(x+5)(x-2)=&gt;y=4x2(x+5)(x-2) The above expression exists…

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (х, у) -

A:

Q: Find the following points of intersection.

A: Given that, y=42xy=2x2

Q: Find the equation of the family of curves whose slope at any point (x, y) is 2. y 4. equal to the…

A: We need to find the family of curves. NOTE - As per our guidelines we can not solve multiple…

Q: Find the point of inflection of the curve y= -x^3+x^2-x+1

A: The expression for the curve is given as, y=-x3+x2-x+1 The expression for the point of inflection…

Q: Find the point of the line y = 2x − 1 that is closest to the origin.

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Q: Find the slope of the curve at the given point. y=2x^3−3x @ (-1,1)

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Q: What is the equation of the radical axis of the curves x^2 + y^2 – 1 = 0 and x^2 + y^2 – 6x + 6y +…

A: Let us consider the curve C1 and C2 To determine the Radical axis between the curve solve  C1-C2=0…

Q: Two is the slope of the curve y = 4x + x2 at what point?

A: Slope of a curve is given by m=dydx  Use this formula to solve above question.

Q: The length of the curve 4/2 3 y = xi - 1,0 < x < 1 is .

A: Given,            The length of the curve y=423x32-1 , 0≤x≤1 is 136.To find : Check whether the…

Q: Find the point on the line  y = 5x + 2  that is closest to the origin.

A:

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.