6. Let f(x) = 20/(x6 + x4 + x² + 1). %3D (a) Show that for any k e [5,20], there is a point c e [0,1] such that f(c) = k. (b) Show that for any k e (0,5], there is a point c > 1 such that f(c) = k.

Q: Consider f(r) 3- 2x and the graph of g below. Suppose p(x) = f(x)g(r), q(r) = f(x)/g(x), and c(x) =…

A:

Q: 04) Find: V2 +7 - 4x a) Horizontal asymbtote for f(x)D x+3 x² - 4 f(x) a to for

A: Given: a) Horizontal asymptote for f(x)=x2+7 -4xx+3 b)Oblique asymtote for f(x)=x2-4x-1

Q: Let g(x) = e² · (x² – 9), g' (x) = e" . (x² + 2x – 9), and g" (x) = e² · (x² + 4x – 7) , Choose one…

A:

Q: Question#1: Determine the singular point(s) of the given DE and classify each singular point(s) as a…

A:

Q: ) For what value of x the function is not defined? e) Evaluate: g(5) – g(-3) n Describe the graphs…

A: This question is related to function, we will solve it using given information.

Q: 1. Find all values of x where a) f(x) = 0, b) f(x) > 0, and c) f(x) 0 when c)f (x) <0 when

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Q: 3. Find [g f](x) for f(a) = 2x +5 g(2) = 2 – 3. and

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Q: Find the domains of h(x)=1/(x3+1)1/3.

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Q: The range of f(x) 3 (2х — 1)(1 — 3х) + 4x2 is О 44/9, со) О -со, 35/9] О 23/5, со) О 17/3, со) О -о,…

A: Given  fx=2x-11-3x+4x2 Here we have to find the range

Q: 1. reasons. Evaluate the limits if it exists. If not, give (a) lim x → 0+ 2 x² −1+ sin(cos¯¹x) x³…

A:

Q: Find the residues of a function 1 f(z) 3 (z − 2)(z + 1)³

A:

Q: 4. For f(x) = x² – 3x, evaluate a) f(2) [2,3,3] c) the value of x when f(x) = 4 b) f(m + 1)

A: Given,              f(x)=x2-3x

Q: Given that f(x) = 7x + 5 and g(x) = 8 – x², calculate (a) (f o g)(0) = f(g(0))= (b) (g o f)(0) =…

A:

Q: Find the constant c that makes g continuous on (-0;0) x-2x-8 g(x) = a+1 if x+2 if X=-2

A: Continuity of a function at a point x=c : If function is defined at x=c and limx→c fx=fc then we can…

Q: Sketch a graph of f(x) (2x - 1 if x 2

A: To sketch the graph f(x) ={  2x-1 if x&lt;2               x-2  if x&gt;=2 for x&lt;2, y=2x-1…

Q: 2) The graph of f (x) = 0.5x(x – 4) (x – 7) is given below. d h a) Draw on the graph the local…

A:

Q: Q2. Given that f(x) = |6 – 2x|. Draw the graph of f (x) and hence evaluate f f(x)dx. [ Fig 1

A: Let's find.

Q: Given the functions Ax) = x+3 and g(x) = x + 2x- 8, determine the domain of the combined function y…

A: For real valued function domain is the subset of real numbers on which function is defined and has…

Q: Which of the following represents the graph whose shown? y= f(x)

A: the first zero is x=A and with a multiplicity of 3 so the factor is  the second zero is x=B and with…

Q: Let f (x) =: 5 +e'+ tanx+ 12*+Vx. Find f (x). For the toolbar, preco

A: On solving this we will get

Q: For the function f(x) = 2, find f'(x). 5/x+2 4 1

A: Given:   f(x)=x+245   To find: f-1(x)

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.