Write the equation of the cone with the top point (1,2,3) and t he rectification curve fx= cost,y= sint, 2=0f

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: Find T, N, and B for the curve r(t) = (10t, 10t, e') at (0,0, 1).

A: Given: we have ,

Q: Find an equation of the tangent plane to the surface z = 5y – 4x? at the point (-4, 2, -44).

A: The solution is given as

Q: Find the exact coordinates of the lowest point and the leftmost point on the curve I = t – 5t, y =…

A:

Q: Find equations of both the tangent lines to the ellipse x2 + 4y 36 that pass through the point (12,…

A: see below the calculation and answer

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

A:

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

A:

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. =…

A:

Q: Find an equation of the tangent plane to the surface at the given point. - 2xy + y², (3, 5, 4) eBook…

A:

Q: Find the points on the parametric curve c(t) (3t2 - 5t, t3 - 10t) where the tangent line has slope…

A: Given curve is Firstly, we find dy/dx

Q: Find the equation for the tangent plane to the surface at the indicated point. -4x – y+ 2z = 1, P(1,…

A:

Q: Do the curves ri(t) = (t² + 3, t+1, t² – 5) and rž(s) = (4s, 2s – 2, s + 1) intersect? If so, at whi…

A:

Q: Find the exact length of the curve. = 플Vy (y-3), 4sys 16 3

A:

Q: Describe the shape of the curve x = 3 cost,y = 3 sin t.

A: We have to describe the shape of the curve x=3cos(t) ,y=3sin(t)

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t at t = 0.…

A:

Q: Evaluate given that F (7, y) = 2yî + (zy – 2r)j and Cis the curve in the third quadrant from the…

A:

Q: 1. Eliminate the parameter in the following and sketch the curve. Indicate the orientation. a) r…

A:

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

A:

Q: Find an equation for the tangent plane to the surface 2? – ry? = 0 at the point G, 2, 3)

A:

Q: Find the equation of the tangent plane to x2 the surface z = 4 + y? at the point (2, –2, 5)

A:

Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: Find a rectangular-coordinate equation for the curve x = 2cos(t) and y = 3sin(t), 0 <t < 2n.

A:

Q: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

A:

Q: Find an equation of the tangent plane to the surface at the given point. 2 x2 + 2z?ey - x = 33, P =…

A:

Q: Find the arclength of the curve z = 8t - 9, y= 15t - 1 with 6 <t<9.

A:

Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

A:

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: Evaluate ∫C x ds, where C is the parabolic curve x = t, y = t2, from (0, 0) to (2, 4).

A: Given: Parabolic curve x=t, y=t2 from (0,0) to (2,4)

Q: Find the tangent plane to the equation z 5z° + 4y – y at the point (4, 2, – 66)

A: Given: z=-5x2+4y2-y      4,2,-66

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

A:

Q: Sketch the curve x = 3sin2t, y = 4cos2t

A: This question is taken from the function in which we have to sketch the given function parametric…

Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

Q: Evaluate SF dR given that F (x, y) = 2yî + (xy – 2x)) and C is the curve in the third quadrant from…

A: Given

Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

A:

Q: Find the arclength of the curve: y = 5(x + 2)3/2,2 <x<7

A: The arc length is given by, S=∫ab1+f'x2dx   Find the derivative of the function y=5x+23/2.…

Q: Find the equation of the tangent plane and normal line to the surface at the given point. x2 z = 9…

A:

Q: Eliminate the parameter to find Cartesian equation of the curve: x=2 sint, y = 5 cost, -n <t<n 6. a

A:

Q: Sketch the curves below by eliminating the parameter t. x = V3t + 4, y = 3t + 2

A: Given query is to sketch the curve by removing t.

Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Find the equation of the tangent plane to the surface z = 4.x*y? + 2y at point (1, -2, 12).

A:

Q: s to the curve y = x* at the %3D

A:

Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Find an equation of the tangent plane to the surface z = y? - x² at the point (-4,5,9).

A: Finding partial derivatives with respect to x and y for finding plane equation.

Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6x² + y² -…

A: This question is based on finding equation of plane to the given surface at a point.

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2, - 5) and…

A:

Q: Find the equation of the tangent plane to the surface z = +y? at the point (2, –2, 5)

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.