3. For the curve y 3*thx at the point (1,1) find the following using exact numbers:

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 the length of the curve y = 3/2 from a = 0 to a = 3.

A: Given curve is y=43x32   Length of the curve is L=∫ab1+dydx2      ......1 Here given a=0 and b=3 and…

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

A:

Q: The line -8x + y = m is tangent to the parabola f(x) = nx² when x = 5. Find the values of m and n.

A: NOTE: Refresh your page if you can't see any equations. . the given tangent line is  here we have…

Q: The tangent line to the curve x'+y° -9xy=0 at the point (2,4) intersects the y-axis at y =. Write…

A:

Q: Find the length of the curve. r(t)=(8t,t^2,(1/12)t^3),0 (less than or equal to) t (less than or…

A:

Q: -4x Find all the values of x at which the curve y = xe has stationary points. %3D Give your answer…

A: The stationary point for a function y=f(x) is the value of the independent variable that is x,…

Q: 3 2 1 Y from y = 1 to y = 11 - 3. ||

A: To find the arc length of the curve x=y323-y12 from y=1 to y=11. Result: Length of a curve y=f(x)…

Q: Consider the curve defined by x = 2t – 1 and Y = 2 – t, for –5 <t< 3. Find an equation in X and Y…

A:

Q: 5.) y=500/[1 + 24e(-.26t)] with an inflection point at t=12.2 Sketch the graph and its inflection…

A: We find y\\' using exponent rule and chain rule.

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.