F and H are sets of real numbers defined as follows. F = {w | w< 4} H= {w |w< 5} Write FU H and FN H using interval notation. If the set is empty, write Ø. (0,미) [□,미 (,미 [0,0) (0,0) FUH = [0,0) FO H = -00 8.

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: F and H are sets of real numbers defined as follows. F={v|v<3} H= {v|v≤5) Write Fn Hand FUH using…

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Q: (2) If h is defined by h(x) = |x| +2, (a) What is the range of h if the domain of h is the interval…

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Q: Let R, - {r E R|1 5 x3 x < 1 for each positive integer i. (Enter your answers using interval…

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Q: The domain of h(x) 7 - consists of all real numbers except 0 and 3, represented in interval notation…

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

Q: I are sets of real numbers defined as follows. = {x | x > 2} %3D n H and FUH using interval…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x s(x) =4x…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows.  r(x) = x-5 s(x)…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = x + 2 s…

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Q: 1a. Show that for the closed interval [a, 6], its set of interior points is the open interval (a, b)…

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Q: A and B are sets of real numbers defined as follows. A-(: |2> 2} B-(: |258} Write AnBand AUB using…

A: Solution:   Given that A &amp; B are sets of real numbers such thatA = z | z&gt;2B = z | z≤8

Q: Determine whether the Mean Value Theorem can be applied to the func- tion on the given closed…

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Q: Given that |f'(x)| < 1 for all real numbers x, show that If(x1) – f(x2)| < \x1 – x2| for all real…

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Q: The interval ___________ consists of all real numbers for which x ≤ a.

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Q: Suppose that the possible values of æ is the interval (-3, ). This means that: - x -3 -3 < x < 3

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

Q: F and H are sets of real numbers defined as follows. F={v|v<4} H={v]v<6} Write Fn H and FUHusing…

A: F = v|v&lt;4H = v|v≤6F∩H = those element/numbers continued in both F and H

Q: Suppose that the functions g and h are defined for all real numbers x as follows. Write the…

A: Given:- g(x)=5x3 ,h(x)=x2  To find:- (g-h)(x)  (g+h)(x) (g•h)(-2)

Q: If an inflection point of the aurve f(x)=acos(2x) +bsin(3x) is P(n /6,5), then what are the real…

A: The given function is fx=acos2x+bsin3x. Substitute the point x, y=π6, 5 in fx=acos2x+bsin3x.…

Q: R.1. Use the Schröder-Bernstein Theorem to prove that the intervals [0, 1) and (1, ∞) on the real…

A: The trigonometric tangent function sprang to mind first, and a strategic linear transformation of…

Q: The domain of a relation R is the set of real numbers. x is related to y under relation R if…

A: We will find out the required solution.

Q: (a) Let S be a set of real numbers with the property that if x1, x2 € S, then the midpoint (x1 + x2)…

A: a) Let S be a set of real numbers with the property that if x1,x2∈S, then the midpoint 12x1+x2 also…

Q: Suppose that the function h is defined, for all real numbers, as follows. 1 *-2 if x2 4 Find h(-1,,…

A: The given function is,h(x)=-14x-2if x&lt;-1(x+1)2-2if -1≤x≤2-14x+2if x&gt;2

Q: F and H are sets of real numbers defined as follows. F={y|y21} H= {y |y>7} Write FUH and FnHusing…

A: A set is a well-defined collection of objects. The objects, which belong to the set, are called…

Q: ollows. h (x) = 1/4x +1     if x 2 Find (0), h (2), and h (5).

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x+6 s…

A: Given : rx = x + 6sx = 4x + 4

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) =…

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Q: Suppose that the functions r and S are defined for all real numbers x as follows. r (x) =x-3 s (x) =…

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Q: Find a function f and a real number a such that

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Q: Show that [x+y] ≥ [x]+[y] for all real numbers x and y.

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Q: Find functions f and g from the set of positive integers to the set of real numbers such that f (n)…

A: Here, we need to find functions f and g from the set of positive integers to the set of real numbers…

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 4x-6…

A: Calculate r-sx. r-sx=rx-sx               =4x-6-x-3               =4x-6-x+3               =3x-3

Q: Z is the set of integers, R is the set of real numbers. 1. Functions f, g, and h are defined as f:R…

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Q: (2) If h is defined by h(x) = [x| + 2, (a) What is the range of h if the domain of h is the interval…

A: (a) , (b).

Q: Prove this: There is a one-to-one correspondence between any line and the set of real numbers.

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Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

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Q: Z is the set of integers, R is the set of real numbers. 3) Each function f is defined as f: R -> R.…

A: The objective is to find the function is one-one or not one-one. (a) fx=x+1x-1for all real numbers x…

Q: (2) If h is defined by h(x) = |x| +2, (a) What is the range of h if the domain of h is the interval…

A: Given function is hx=x+2 Graph of the function can be drawn as,

Q: Suppose that the functions g and h are defined for all real numbers x as follc g(x) =x+4 h(x)=2x…

A:

Q: If h is defined by  h(x) = |X| + 2, What is the range of h if the domain of h is the interval…

A: The given function is h(x)=x+2

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) =…

A: Given  rx=6xs(x)=2x+3 where the expression for r+sx,  r-sx  and  r·s2 is to be evaluated.

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: a) In the set of real numbers A = {x | | x - 2 | > 1, x E IR} cluster is given. Accordingly, express…

A: 1) A) The given set is: A={x||x-2|&gt;1,x∈ℝ} Here,  |x-2|&gt;1⇒x-2&gt;1 or x-2&lt;-1⇒x&gt;3 or…

Q: The domain of g(x) =3/(x - 2)consists of all real numbers except 2,represented in interval notation…

A: To Determine: The domain of g(x) interval notation as (- ∞, 2) ∪________. Given: we have a function…

Q: Suppose that the function h is defined, for all real numbers, as follows. 1 2 if x<-1 h (x) =< -…

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Q: Let the universal set be the set R of all real numbers and let A={xeR|-2<x<2} and B= {xeR|-3<x<1}.…

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Q: Let the function f be defined by y = f(x), where x and f(x) are real numbers. Find f(2), f(−5),…

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Q: Suppose that the functionh is defined, for all real number 1 2 x++5 if x -2 h (x) = < %3D -3 if x…

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Q: The domain of the relation A is the set of all real numbers. Ay if |x-y| ≤ 2

A: Given relation is A=(x,y): x-y≤2, x,y∈ℝ Here x is the domain of the relation.

Q: 1 -Find all the points where f(2)is analytic. 2+3 Let /(2) =

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Q: Z is the set of integers, R is the set of real numbers. 2) For each of the following functions…

A: a) Here, f: Z -&gt; Z, f(n) = n - 6

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.