f(x) = 4 – x² g(x) = 5x – 20

Q: Find the slope of the curve y =x' – 2x at the point P(2,-2). .3 4

A: Given the equation of the curve,                                           y=14x3 - 2x and the point…

Q: 2x +1 Find the slope of the line tangent to the graph of y = 5x at x = 1. 4

A:

Q: Describe each of the following curves: r2 = 2

A: We know that, each point x,y in the Cartesian coordinate system can therefore be represented as an…

Q: Graph the following curves and determine the x and y intercepts. y + x = 5 1.2 1.1 y2-3x = 0 1.3 y +…

A: (1.1) We have the given equation of curve as y+x=5 On taking the ordered pair or data points, we get…

Q: Use the steps to curve sketching to graph the following functions 3.) f(x)=x²-12x+36

A:

Q: Use the point-slope equation to identify the slope and the coordinates of a point on the line y – 4…

A:

Q: b. Find the equation of the circle if its diameter has an end points of (6, 1) and (-2, 3)

A: According to guidelines we should have been able to solve only one question at a time #b

Q: (e) (f) lim X118 lim x→+∞ f(x) = f(x) =

A: Given that the graph of the function f(x). to determine the following limits.     and

Q: Y = x2-4)2 X-4

A: Explanation: Given that, y=(x2-4)2x-4 x-intercepts are: 0=(x2-4)2x-4(x2-4)2=0(x2-4)=0x2=4x=±2 Graph…

Q: Find betwee y = x2 the the CurveS and area 2. 3= 4x-x groph %3D Draw

A: Given curves :

Q: y = cearcsinx +c2e¬arcsinx

A:

Q: For the function, find the point(s) on the graph at which the tangent line has slope 4.

A: The slope of a line is equal to the tangent of the angle that the line makes with the x-axis. The…

Q: Find an equation to model the vertical motion of the tip of a second hand on a clock, if the second…

A:

Q: 3. Trace the curve: y² = x³ + 4x² - 9x - 36

A:

Q: c. Find the equations of the line tangent to the curve y = x³ + x, where the slope is equal to 4.

A:

Q: Use a graphing device to graph the curve x = y4 - 3y2

A: Given curve:

Q: Find the distance from the point (4, 9) to the line y = 2x.

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.