{x|x EN and 15 is less or equal to x<60}

Q: = 1+ x+x?. . Show that ifx is se smail that x and higher powers can be neglected, then:

A: Note : Since you have asked multiple question, we will solve the first question for you.

Q: Prove or disprove the statement: For all x E R, |x + 1| + |x – 1| > 2.

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Q: 3/4 Given: 4 2x+ 35 Prove: x= 4

A: Given: 42x+34=35

Q: Find the derivative

A: Given function is  By using the properties of log  log(m)-log(n)=log(m/n) and log (m^n)=nlog(m), we…

Q: Find a positive number x such that the sum of 4x and is as small as possible. Does this problem…

A: Solution is given below:

Q: 6-Given P(x)=2x3+3x2+1 and Q(x)=8x-2, find all the possible values of so that Q(x)<P(X )state your…

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Q: Show that the multiplicity of (x-1) is 1.

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Q: For all number x, x>1/x

A: We have the relation : x &gt; 1x

Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

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Q: If n is any real number and f(x) = x", then f'(x) = nx"-!

A: Why does ddxxn=nxn-1                 ddxfx=limh→0fx+h-fxh…

Q: Give the domain of s(x)=x2+2x√16−5xs(x)=x2+2x16-5x in interval notation

A: Given the functions(x)=x2+2x16−5x

Q: Find all real numbers  x such that  x^6−3x^3−18=0. Give your answers in increasing order.

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Q: الواجُب (x-1) (x+4)<o 2 )و - رصه - (

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Q: given 7(x-1)=2(3x+2) prove x=11

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Q: If f(x) <0 for all real numbers x then f is decreasing or increasing on its interval?

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Q: a) Solve for x in the following questior 7-x = 1 %3D

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Q: If ƒ(x) is odd, can anything be said of g(x) = ƒ(x) - 2? What if ƒ is even instead? Give reasons for…

A: Given function g(x) - g(x) = f(x)-2Given function f(x).If f(x) is odd then,f(x) =-f(-x)Substituting…

Q: If x is any real number, then cosh x Σ n=0 n! + 198 Σ n=0 (-x)" n!

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Q: (b) Expand and simplify in ascending powers of x as far as the term in x" 1+3x

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Q: 4. Find all values of x satisfying In[(2x + 1)(x +2)] = 2 In(x+2). Verify the values of x you found…

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Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

Q: 4. Find all real values of x such that |x-1| > |x+1]. * (-00,-1] (-00,0) [-1,0) [-1,1) None of the…

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Q: f(x) x* + 3x - 3x + 2 %3D as x -00 f (x) → 0 as x -of (x) → -∞ as x +∞f(x) → -∞ as x → +of(x) → +o

A: Given polynomial f(x) =-x4+3x2-3x+2

Q: 3. Given that g(x) =7x-6 and f(x) =x+1, then the domain of |(x) is O{r\x&R} O{r|x+-1, xɛR} xɛR 6 -1,…

A: First I have written the definition of qutient of two functions and tell about their domain. Option…

Q: of t/4 for x. (If an answer is undefined, enter UNDEFINED.)

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Q: (c) Prove that x - 11 |x| + 11 |x² + 36| 36 for all real r.

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Q: Excrcise 8. Evaluate -In 2 xe d.x 1

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Q: Given: 3(x + 2) = 15 Prove: x = 3

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Q: 3 6. Let A= 0 x+1 1 x -8 x-1 For what values of x does A-¹ exist?

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Q: The product of any non-zero rational number and any irrational number is irrational. For all real…

A: To prove the statement by using the method of contradiction, first assume that the conclusion is…

Q: Let x² – x – 2 h(x) = x² + 4x Find all the values of x that are NOT in the domain of h.

A: For a rational function, denominator should not be 0.

Q: The set of all real numbers x for which x24x+2+x>0 is

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Q: 2- Let g(x) = x5 - 8.6x* + 38.782x3 - 17.25x² - 4.5927x + 10.5 then the value of g(0.25 x 101) =…

A: The objective is to state whether the statement is true or false. For the polynomial…

Q: termine k such kx2  _ 4x + 1/2 + 0 that has real and different solution

A: To determine the value of k such that the below equation has real and different solutions.…

Q: a? - 1 x² + 2x+- at -5' x+2 ;x>0 Let f(x) = { Find all possible real values of a such that f(x)…

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Q: Suppose that 0 &lt;ƒ′(x) &lt; 1/2 for all x-values. Show that ƒ(-1) &lt; ƒ(1) &lt; 2 + ƒ(-1)

A: From the given inequality the behaviour of the function can be determined as.

Q: If x is any real number, then cosh x = Σ + Σ n! n=0 n! n=0

A: We have to find out

Q: Sketchthegraphofy=x2−5x+4.

A: We first make a table for y=x2 −5x+4 x 1 2 2.5 3 4 y 0 -2 -2.25 -2 0

Q: real numbers such that a < b. <x < b} is uncountable. <x < b} is countably infinite.

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Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: Find the coefficient of x in (1+x'+x°).

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Q: Suppose f(x)=x^2+3 and g(x)=x-2. Which of the following is a formula er (f-g)(x)? *

A: Substraction of two function

Q: True or false. You must justify your answer. For any positive epsilon and any x, we have…

A: True or false. You must justify your answer. For any positive epsilon and any x, we have…

Q: Find all values of x for which ∑ (n=0 to ∞) 1/(1+x)^n equals 4

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Q: Find the maximum value of f(x)=x^3-3x on the set of all real numbers x satisfying x^4+36< (less then…

A: Given: The function fx=x3-3x To find: The maximum value of given function on the set of all real…

Q: - 31. P(x) = x³ – x² – 6x 33. P(x) = –x³ + x² + 12x • 35. P(x) = x* – 3x³ + 2x² %3D | · 37. P(x) =…

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Q: For which positive numbers a is it true that a" > 1 + x for all x?

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Q: The average pollen count in a certain city on day x of the pollen season is  P(x) = 8x − 0.2x2…

A: The average pollen count in a certain city on day x of the pollen season is  Differentiating with…

Q: 7. Find all values of x that satisfy the given conditions: f (x) = 2x – 5, g(x) = x² – 3x+8, and…

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Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.