Consider the following. x = tan?(0), y = sec(@), -x/2 < 0 < x/2 %3D (a) Eliminate the parameter to find a Cartesian equation of the curve. (b) Sketch the curve and indicate with an arrow the direction in which the curve is traced as the parame y y 3.0 3.0 2.5 2.5 2.0 2.0 1.5 1.5 1.0 1.0 0.5 0.5 0.5 1.0 1.5 2.0 2.5 3.0 0.5 1.0 1.5 2.0 y 3.0 3.0 2.5

Q: Consider the parametric curve defined by x = t – 7, y = t* + 13t. What is %3D - the slope of the…

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Q: 0.7 y(t) = 0.11 cos 7.6t+ sin 7.6t+ 0.17 7.6 y (1) = 0.11 cos 7.6t+ y(t) = 0.11 cos 7.6t+ y(t) =…

A: A graph is used to plot the equation as a pictorial representation. By the graph, it is easy to…

Q: x=sec(t) y=tan(t) t E[0,pi] a) Identitfy the (x,y) coordinates of the point corresponding to the…

A: To determine the coordinates of the point.

Q: x = 7 te', y = (t + 1)e', 0stsi Set up an integral that represents the area of the surface obtained…

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Q: Consider the parametric equations x = 2t – 5, y = 6. dy Use the derivative formula from Section 10.2…

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Q: For the parametric curve given by x = t + sin 2t, y = cos 2t, dy d²y (i) calculate the derivatives…

A: Given parametric equations: Objective: To calculate the derivative of and .To find the equation of…

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Use a graphing utility to graph the curve defined by the parametric equations x(t)=3t sint, y(t)=3t…

A: It is given that xt=3tsint, yt=3tcost with 0≤t≤2π. The objective is to choice the correct graph from…

Q: The parametric equation of the motion of a particle on a plane is given by 3/2. x = te + 2t12; y=t'…

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Q: Sketch the graph defined by the parametric equations x = e' -t and y = 4e? for 0st<2. Indicate on…

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Q: Consider the family of curves described by the parametric equations x = a cos t + h, y = b sint + k.…

A: The parametric equations of a curve in two variables are obtained when both the variables of the…

Q: b) The length in first quadrant of the curve x/3 + y2/3 = a²/3 is given by 6ac/2 where parametric…

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Q: The equation of the tangent line to the parametric equations, x = sine, y =20+ cose at e = 0 is y =

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Q: Find for the parametric curve x= 2e', y= sin(1+ e') dx

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Q: Without using a graphing utility, show that the parametric curve r(t) = (3t cos(3t), 3t sin(3t), 3t)…

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Q: 6. Find parametric equations for the tangent line to the curve z-int, y = 2√t, z = ² at (0,2,1).

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Q: 1. Express the given parametric curve by an equation in x and (a) x = 8t²-5, y = 2t - 1, for t€…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

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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.