(2) Prove that (1+x)" > 1+nx for all x > 0 and n > 1.

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: 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: Find a point c satisfying the conclusion of the MVT for the func y(x) = 2e* on the interval [0, 5].…

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Q: 1. Use the Intermediate Value Theorem and Rolle's Theorem to show that the equation 3x + 4* = 0 %D…

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Q: (n² – 3n – 21) ÷ (n –7) -

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Q: b-a Use the theorem (≤ ) to find a bound for the number of iterations needed to achieve 272 an…

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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: Problem 3.2 Let æ be a real number. Show that [3r) = [r] + ++++

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

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

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A: We need to find the asymptotes of the given function.

Q: 5n – 9n3n lim (4п)2n + 17 n-00

A: Note the results : that is    Product rule of limit : If at least is one of them is non -zero…

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: Which of the following is a critical number of f(x)= 4. 2x %3D

A: The given functIon is: f(x)=14x2-2x

Q: a. Use the Bi-section method, to approximate v2 in three steps in the interval (1,2| (use 3 digits…

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Q: 10 3. Prove that the L{10e2} = s-2

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Q: 1. In the figure below, find the number(s) "c" that Rolle's Theorem promises (guarantees). y-fx) 5…

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Q: Prove that L ={(1Z*)"10" | n e N}is not regular.

A: The given language: Then, the above language can be rewritten as, To prove that L is not regular.…

Q: Let ƒ(x) = (x - 2)^(2/3). a. Does ƒ′(2) exist? b. Show that the only local extreme value of ƒ occurs…

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

Q: Knowing that In(1)=0, the correct second order numerical approximation of In(1.5) is ? (Use as much…

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

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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: Theorem 4 Every solution of Eq.(1) is bounded if a < 1. Proof: Let {an} -4 be a solution of Eq.(1).…

A: The (n+1)th order difference equation is…

Q: x : x is a natural number less than 10​}

A: Write in explicit form

Q: ased on its degree and leading 3. G(x) = -2x+ 3x2-x+ 1. %3D Write your description here.

A: As per our guidelines we are supposed to answer only one question please post another question as…

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

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Q: Suppose that a random number  is chosen from the interval (0,2). What is the probability that the…

A: Given: The random number is chosen from the interval (0,2). Quadratic equation is 4x2-x+k

Q: 16. There is a very quick way to compute £-, 2'(-1)ª-' (); do use it. l=D0

A: Introduction: The binomial theorem is very important in mathematics. For any real numbers a,b with…

Q: 3n? is strictly increasing and find an upper bound. n2 + 2 Rigorously show that a, =

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Q: 2. (a) For n ≥ 0 and x E R, prove that (b) Prove n n Σ ^ (^.) 2^* (1 - 2)"-* k k=0 = = In. n x)n-k…

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Q: Find the length of segment NL. N x-8 x- 5 4 K L. 0 4 15 O19 3.

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Q: Prove that the real part of is constant for -n < 0 < n z+2-i

A: Let  z = a+ib

Q: Solve the equation for x In(x+ 1) + In(x – 1) = 1

A: Solve the equation for xlnx+1+lnx-1=1

Q: 2. Assume that x > -1. Prove that (1+ x)" >1+ nx for n = 0, 1, 2, .... %3D

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Q: Find a positive number x such that the sum of 9x and is as small as possible. x = Does this problem…

A: Let, the sum be denoted by f(x) So, f(x) = 9x + 1/x  So, f'(x) = 9 - 1/x² &amp;, f"(x) = 2/x³

Q: The Intermediate Value Theorem can be used to prove that the equation z² - 5x+6=0 has at least one…

A: Given :x2-5x+6=0

Q: For the part highlighted in green, why doesn't negative infinitiy cancel with the negative near the…

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Q: =] Verify n(n + 1)(2n + 1) 6 j=1

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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: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

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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: Q4 Legendra polmomial Pe (X) =2 + (3x+1) than Prove that (2u+1) Puck) =Pmnil (X) -P(X) n-1

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Q: The characteristic of Zs[x]/ is 6. 3 O None of the choices

A: The characteristics of the function

Q: For any real number x, x 6| + x > 3.

A: Case I :  x≥6x-6≥0LHS=x-6+xx-6+x2x-62x-3≥26-3≥6&gt;3=RHS

Q: Find the value of K that make s the funtion fcx) Continus : x*+ 3K メニ2; %3D 2K-X > 2

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

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