Consider the following. f(x) = -3x-2; a = 2, b = 6 (a) Calculate the total area of the region(s) between the graph of fand the x-axis from a to b. (b) Evaluate (x) dx. (c) Explain why the result from part (a) differs from that of part (b). When a graph of a function lies ---Select--- e the horizontal axis over an interval, the definite integral is the ---Select--- of the area of the region between the graph and the ---Select--- axis.

Q: says "determine wheather the point lies on the graph of a function"…

A: We have to check whether the point lies or not

Q: How is derivatives utilized in solving for the dimensions and total area of a box?

A: Here we to write how is derivatives utilized in solving for the dimensions and total area of a box.

Q: ind the exact location of all the relative and absolute extrema of the given function: h(t)= 2t^3…

A: find critical point and check sign of double derivative at critical point

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A: Givenf(x)=x2-2x

Q: Two functions are defined as follows: f(x)=7-2x² and g(x)=x²+4 (a) Use ANY graphing tool to…

A: Here We have to find the point of intersection of the two curves.

Q: Using four triangles to estimate the area under f(x) is approximately

A:

Q: Find the area between the curve y = x² + 12x + 27 and the x-axis from x = -3 to x = -1.

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Q: Use the graph of f(x) below to put the values of f'(-6), f'(0), and f'(2) in decreasing order. 2.5…

A:

Q: for a function f, the forward-divided differences are given by 1, - 0.0 X = 0.4 S, xal = 10 = 0.7 al…

A:

Q: Consider the following. f(x) = 11(0.85*); g(x) = 7(0.75*); a = 2; b = 10 (a) Sketch graphs of the…

A:

Q: Given that f(x)= x^3 - 2x^2 + 1, for a domain of [-0.5,2.1)

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Q: For the function f(x)=1/4-x^2, find the horizontal and vertical asymptotes.

A:

Q: help me understand this.    F(x)= 3x-x^3 what is/are the x-intercept(s)?  what is the y-int? what is…

A: Given, y = F(x) = 3x - x3 For x-intercepts, y=0 ∴ 3x - x3 = 0 =>x(3-x2) = 0 =>x = 0, √3, -√3 ∴…

Q: (a) Graph the IL f(x) = in the viewi (b) Using the g a rough ske Example 2. (c) Calculatef Compare w

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Q: Find f. f"(x) = 4x3 – 6x² + 5, f(2) = 1, f'(3) = 2 %3D

A: Here, f''(x)=4x3-6x2+5⇒f'(x)=∫(4x3-6x2+5)dx+C             =4x44-6x33+5x+C             =x4-2x3+5x+C…

Q: 2. Rectangular box is inscribed in a sphere of (a) Set up a function of 2 variables that describe…

A: Given That: sphere of Radius 5 in  To Find : a) a function of two variables that describe the volume…

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.