Suppose x is a real number. Prove that if x 2, then there is a real number y such that x = (2y + 1)/ (y- 1). %3D

Q: Find the axis of symmetry: f(x) = x-5x+6 O x = -5/2 O x = 5/2 O x = 1/4 O x = -1/4 ype here to…

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Q: If h(t) t" where n is a natural number, then what is h'(t)?

A: If h(t)=tn, where n is a natural number then our aim is to tell the valueof h'(t)=?

Q: z = If X – y show that: =D0

A: Given: z=xyx-y And x2∂2z∂x2-y2∂2z∂y2=0   As we know that; The Quotient rule; fg'=f'·g-g'·fg2 The…

Q: Determine all values of x so that det(A) = 0, where A =

A: Given: The matrix A is x12x. Calculation: The determinant of the matrix x12x can be obtained as,…

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: 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: a. Prove that ex>= 1 + x if x>= 0. b. Use the result in part (a) to show that ex>= 1 + x +…

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Q: ketch represents f(x) = x² + x – 6 and g(x) = -x - 3 M If MN = 3, calculate the possible length(s)…

A: Graph for a function is representation of function with respect to independent variable on axes.…

Q: For which values of a does x + a = 0 have a solu­tion in Z5?

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Q: y If z = show that = 0. x + y?*

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Q: Show that for all x, e* > 1 +x.

A: It is given that, ex≥1+xwe have to show that for all x.

Q: Let ƒ(x) = | x3 - 9x|  . a. Does ƒ′(0) exist? c. Does ƒ′(-3) exist? b. Does ƒ′(3) exist? d.…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: consider this formula. z= y over x if z= 4.0 and y=6.0  express your answer to the tenths place

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Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: If f(x) = 3x — 7, find the image of 2 and the preimage of 2

A: Given: fx=3x-7 To determine: Image & pre-image of 2.

Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: For ƒ(x) = sin x, find ƒ"(x), ƒ″(x), ƒ‴(x), and ƒ(4)(x). What is ƒ(4n)(x) when n is a nonnegative…

A: Given  f(x)= sinx Lets take first derivative f'(x)= cos(x)f''(x)= -sin (x)f'''(x)=…

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: Show that for any real constants a and b, where b > 0, (n + a)» = ©(nº)

A: To show for any real constants a and b where b > 0, n+ab=Θnb

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

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Q: if f (x) 9-x and g (x) = Vx, then the domain of (gof) (x) is: [-3,3] O [0, co0) O (-00, c0) O (-0,…

A: on solving this we get

Q: x is the distance 1:- Show that the from morm Il x|l o7 2 to

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Q: Find the domain: f(x) = In(3 – x).

A: A function is a relation which maps each element in its domain to exactly one element in its range.…

Q: The characteristic of Z3[x] is 6. a) True b) False

A: Determine whether the given statement is true or false.

Q: f(x) = In (1+x³)

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Q: 1. If k is a nonzero constant real number, then the statement y kx implies that y varies as x.

A: Given : y=kx, where k is nonzero constant real number

Q: af 10x +11ly and = 11x. Which of the following is the best definition of (x,)) = If %3D Əx

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Q: Find the value of x in Q. x=___

A: A line perpendicular from centre of a circle to the chord is bisect the chord.

Q: Let f(x) = x³ + x + 4 and g(x) = 2x + 3 in Z, [x]. Then the remainder when dividing f by g is: O 4

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Q: Show that there is a real number t such that (e^−t) − (t^3) = 207/(t^4) + 1.

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Q: If k> 0 such that k S x 8k dx = 7 then

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Q: сх* — 4 if x2 x > 2

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Q: For any natural number m, evaluate 1/m +x")( 3m 2m 2m +x 2x +3x" +6)"* dx, x > 0. m X

A: Topic:- Integration

Q: Show that 2Vx < e* for all real numbers x.

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Q: Given that -ax- Y(x): exp %3D 2 a) Calculate for n even

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 3. Given that fæ) is continuous for all real numbers, find the value of "a" & “b". 2ах + 3b , х<1 =…

A: It is known that if function is continuous for all real numbers, then left-hand limit and right hand…

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

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Q: Given an interval [a,b] that satisfies hypothesis of Rolle’s theorem for the…

A: Given function is x3-2x2+3 .

Q: Suppose that Y = Z - X is independent of Z and of X. Show that Y is a constant.

A: Given that Y=Z-X. To show: Y is a constant function.

Q: Q4/ If A = 3 - l: prove A-A-5I = 0

A: Given that: A=213-1

Q: (2) Find the value of ß (,-)

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Q: Prove that if æ - Exp (A), then E (x) = X. 2~

A: Here,x~Exp(?)

Q: x | X> 3) =? and E [X | X> 3] =?

A: X ∼ exp (λ)  having pdf  f(x)=λe-λx      x&lt;0

Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: 2. Use a theorem to find the ff. Zx if yz? + z = 5xy – 1.

A: Find out the zx when function is given as yz2+z=5xy-1 or yz2+z-5xy+1=0

Q: Find The coefficient cof x ard X in The expasion of Ox°-)

A: We have to find the coefficient of x9 and x10 in the expansion of given series.   According to our…

Q: Let x be a real number. Show that 1 [3x] = [x] + | x + - 3 3 ++1+

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Q: (c) Show that for each real number x, | cosh(x)| < el and | sinh(x)| < el*l. (d) Show that for each…

A: Solution of part (c): coshx=ex+e-x2=12ex+e-x≤12ex+e-x But ex≤ex and e-x≤ex, ∀x∈ℝ Therefore,…

Q: Find a number 8 such that if |x – 2| < 8, then |4x – 8| < ɛ, 11) where ɛ %3D 0.01.

A: Ffind the delta