Prove in detail that if A has infimum 2 then B={x∈R|∃a∈A, x=3a} has infimum 6.

Q: Find one real root of g (x) = In(x*) = 0.70 between 1 and 2. How many number of iterations were…

A: Given function is gx = lnx4 = 0.70 when   lnx4 = 0.70⇒lnx4 - 0.70=0⇒ hx = lnx4 - 0.70 initial…

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f (x) =² – 6x + 8 on the interval…

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Q: Let = e²i/n be an n-th root of unity. Show that (k(1-n) Resck (27²1) n for all 0 <k<n-1. =

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Q: a. Prove that ex&gt;= 1 + x if x&gt;= 0. b. Use the result in part (a) to show that ex&gt;= 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: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, ....

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Q: Suppose h is continuous on ℝ and h(q) = 0 for every rational number q. Does it follow that h(x) = 0…

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Q: - - 9. - [1.0001 x* H. Verify Let A 6 = the error %3D 1.0001 formula |r* – ô|| ||r|| < K(A)-

A: Let A=2112, b=33, x^=1.00011.0001, x*=11. Verify the error formula x*-x^x*≤KArb.

Q: Show that for all x>0, e* >1+x+÷ 2.

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Q: Vx4 + 39x + 13 – 4 = 0

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Q: The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration method (i) Xk+1 =…

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Q: Find (with proof) the infimums of the sets S = {1 / n : n  ∈ ℕ} and T = { (-1)n / n : n  ∈ ℕ}. Is…

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Q: What can you say about the upper bound of E(x) for numbers of the form 3^(2n) + 1?

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Q: ind the root of f(x) = In(x/2) + 8x with Fixed Point Iteration method. - In (2 ake g (x) and the…

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Q: 4. Prove that if f(x) = aox" + a,x"-1+ ...+ an-1x = 0 has a positive root x = xo, then the equation…

A: Roll's theorem: If f is continuous function on [a, b], differentiable on (a, b) and f(a) = f(b) then…

Q: In calculating the approximate value of the fourth root of 624, which of the following approximation…

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

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Q: Prove that P(X = n) = 1. 00 %3D

A: Given that  We have to proof that  ∑nP(X=n) =1

Q: Use the Intermediate Value Theorem to show that the following equation has at least one nonzero…

A: Given That,  Sec(2x)= 3^x

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

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Q: a. Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x = 0…

A: Given:Use Taylor’s formula with n = 2 to find the quadratic approximation of ƒ(x) = (1 + x)^k at x =…

Q: a. Use Taylor's formula with n= 2 to find the quadratic approximation of f(x) = (1 +x)^ at x= 0 (k a…

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Q: Prove that if C has infimum 2 then D = {x ∈ R | c ∈ C, x = 3c} has infimum 6

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Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: Let h(x) = e" + 2x. Use the Intermediate Value Theorem to show that e" + 2x = 0 has at least one…

A: First it is required to show that h(x)=0 has at least one solution, where hx=ex+2x

Q: Solve the following Higher Order Non-homogenous DE using Methods of undetermined coefficients…

A: Given,y'' -2y' +y=3x+2A second order linear, non-homogeneous ODE has the form of   ay''+by'+cy=gxThe…

Q: the no of iterations necessary to solve f(x) = x² – 7x + 6 in [2,7] using bisection method and…

A: 21

Q: For any n large enough, prove E" ) – = 0(1). k=0

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Q: a) Prove If he Given DE Is exact or non-exact Find its General solution

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Q: It can be shown that for any a &gt; 0, there is a r such that at=ert for all real values of t. Find…

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Q: Verify that each of the following statements is false by finding a counterexample. x/x =1

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Q: (-1)" n (k) {n+ (m) {r E Q : r² < 4} (0) {x E R: x < 0} :n e N} n

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: Prove that for x&gt;0 the inequality lnx≤x−1 is true.

A: Given data:     The given inequality is: . The given expression can be written as, Here, f(x) is…

Q: Prove thot if yef(x) is continyous and f(x) =0 when x is a ratsonal number, then f(x) =0 for all x €…

A: Given that y = f(x) is continuous and f(x) = 0, x is a rational number. To prove f(x) = 0 for all…

Q: (x – 2)² – In x = 0, [1,2]

A: The given equation is x-22-ln x=0 the formula for the secant method is given by…

Q: Find a positive number x such that the sum of 36x and is as small as possible.

A: We will use basic knowledge of functions, differentiation, and the second term extrema test /…

Q: Formally prove the T(n) = (5n – 4)° is O(n³). Show all work and all steps to receive full credit.

A: Order: T(n)=(5n-4)3 T(n)=(5n)3-3.(5n)2.4+3.(5n).(4)2-(4)3T(n)=125n3-300n2+240n-64

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f (x) = x² – 12x + 35 on the…

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Q: Sove for X: 3+ In(x+2)=2 .do not round any intermediate Computeltions; and round your answer. to the…

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Q: Oprove Heed A A lnda = 2 - - where feass integmle even funchen

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Q: Verify that the hypotheses of "Rolle's Theorem" are satisfied on the given interval, and find all…

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Q: x+1 Q1/ Prove that coth-1 x = 2 x-1

A: In this question we need to show coth-1x=12lnx+1x-1.

Q: 32 For the iteration formula r,n+1 (4.xn +), if xo = 2 what is the value of r3? Prove that lim,n¬00…

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Q: any n > N(\epsilon) | fn(x) - f(x) | < \epsilon

A: The Weierstrass approximation theorem states that every continuous function defined on a closed…

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

A: Here,x~Exp(?)

Q: show that for positive epsilon, |x-4| |3x-12|<e

A: a⇔b implies if a holds then also b holds and vice versa.

Q: x+1 Q1/ Prove that coth-1x = x-

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Q: (a) Verify that the hypotheses of the Mean-Value Theorem are satisfied on the given interval, and…

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Q: (d) Use Taylor's formula to find a positive real number r < 1 such that the error in the…

A: According to the given information, it is required to estimate the error using taylor’s formula.

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,…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.