Calculate the length of the curve defined by x =- Vy(y-3)on the interval 1 < y < 9.

Q: Find the slope of the line tagent to the curve of y = In x/x at point (1,0)

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

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

Q: Find all points (x,y) on the graph of y = X-4 with tangent lines perpendicular to the line y = 4x-…

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Q: [8] Find y' of e'sinx=y/x

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Q: Trace the curve: y= x / (x-1) (x+3)

A: Consider the given function y=xx-1x+3

Q: Find the coordinates of the point/s on the curve y = 2x2 which are closest to the point ( 9, 0 ).

A:

Q: Find the set of values of y=2x+k meets the curve y=1+2kx-x² at 2 distinct points?

A: Given: y=2x+kat 2 distinct points

Q: Determine the length of the curve x = (y-1), where 4 <y <9.

A: Now differentiating given curve with respect to y, we get

Q: Find the maximum point of the curve y= -2x+1 3 2 В. D.

A:

Q: 4) Find the slope of the curve y = 3x + 1 at point P (1,2)

A: We need to find slope of curve at given point.

Q: Trace the curve y = 2x / (x+2) (x-3)

A: Consider the given function, y=2xx+2x-3 (1) First find the domain of the function. So, put the…

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.