1. If f(x) = 3x2/3 - 10, find the arc length of the graph from the point A(8,2) to B(27,17).

Q: Determine arc length of the graph of the equation (y-1)3  = x2 where the interval is [9,11].

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Q: c. Find r' (t) and graph r' (t) on the same graph as r(t). Distinguish each by using different…

A: Please see the below picture for detailed solution.

Q: Find an equation of the line tangent to the graph of y = exat x = 0.

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Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: What is the length of the graph of y = In(x<+1) - x from x = 0 to x = 3?

A: Given  The graph equation is y=lnx2+1-x  from  x=0 to x= 3 .   Formula :- Arc length of curve…

Q: 7- Find the leng thof the Curve arce 34 from to y=4

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Q: What is the length of the arc y = (x6/6) + (1/16x4) on the interval [1,2]?

A: Given, function and interval

Q: 2. Find the equation of the line that is tangent to the circle x + y = 25 at the point P(3,4)

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Q: Find the equation of the tangent to the curve y=√x at the point (1,1) (Figure 4).

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Q: find p'(2) and q'(8) using the graph?

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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.