20. The asymptotes of the curve (x – 5)² (x + 5)(x – 3) y = are A x = 3, x = -5, y = 5 в х3-3, х 3 -5, у %3D -5 -(=3, x = -5, y = 1 D x = 3, x = -5, y = -1

Q: Show that [0, ∞) and (0, 0) ad subspaces of R with the usual topology are not homeomorphic.

A:

Q: The point P(5,-2) lies on the curve y = (a) If Q is the point (x, (1) 4.9 MpQ (ii) 4.99 MpQ (iii)…

A: Given that P(5,-2) and y=24-x the equation of the curve. Q (x, 24-x) lie on the curve.

Q: Q6/At what point on the curve y=x²+8 is the slope of tangent line 16? Then write the equation for…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: y=11-x Also, the given Slope is -1

Q: Consider the function f(x) = 4x − x² and the point P(1, 3) on the graph of f. (a) Graph fand the…

A:

Q: Q3: Find equations of all lines having slope (-1) that are tangent to the curve y = 1/(1-x)

A: Determine the derivative for function y in terms of y and x. The derivative y' is equal to slope m.…

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

A:

Q: 5. Trace the curve: r = 4 cos 0 e (degrees) r e (degrees) r 8 (degrees) r 8 (degrees) r 165⁰ 180°…

A: To Sketch: the following curves: (1) y=x(x-4)(x+1)(x-2) (2) y=x2-4x+4x2+x-2 (3) y2=x3+4x2-9x-36. (4)…

Q: Find a cubic function whose graph has horizontal tangents at the points (-2, 6) and (2, 0

A: Take y=ax3+bx2+cx+d Differentiate with respect to x, y'=d(ax3+bx2+cx+d)dx Since the tangent is…

Q: Use a graph to estimate all the vertical and horizontal asymptotes of the curve y=7- 2x + 1 x' - 2x…

A: y=x3x3-2x+1 The graph is,

Q: 5. Figure Q5 shows the graph y = f(x) on the xy-plane. 54 -5- Figure Q5 (a) Does the graph above…

A:

Q: Find the slope of the curve f(x)= x2 at the point P(2,4)

A:

Q: Find the point on the curve g(x) = x² – 2 that is closest to the point (3,-2)

A: We can represent all the points on the curveg(x) = x2-2 as (x, x2-2)Now we will use the distance…

Q: The points at which the graph of the equation 8x2+ y² – 16x + 8y + 8=0 has horizontal tangent lines…

A:

Q: Determine the horizontal asymptote of the curve y=2x4/(x4-3x4-1)

A: To determine the horizontal asymptote of the curve, y=2x4x4-3x4-1.

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.