To show that r - 1= In(r-r+ 1) has at least two different positive root in R. 6.

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Q: Prove that 1/r + 1/r2 + 1/r3 + . . . = 1/r − 1, for |r|  > 1.

A: we have to prove that: 1r+1r2+1r3+. . . . . .=1r-1  ,  for r>1

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Q: Let f(x) = x2 + bx + c, b is negative odd integer, f(x) = 0 has two distinct prime number as roots,…

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Q: Q2: Iff (z) is analytic at zo. (b) Give an example to show that the converse of (a) is not…

A: If f(z)  is analytic at Z0  Then it must be continuous at Z0  We already prove.  Now we consider…

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

A:

Q: 5**) (a) Prove that for all positive real numbers n, r, and s, if rs < n, then r < Vn or s < Vn.

A: As per Bartleby's answering policy, we can answer only one question, so kindly post the next…

Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

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Q: 5. Use the Intermediate Value Theorem (IVT) to show that the equation below has a root in the…

A: Given that, The function is, f(x) = 2x3 + x2 + x + 3 = 0 interval is = (-2, 0) We have to prove by…

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 13. Prove by Math Induction ex > 1+x for all positive integers x > 1

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Q: 6) The Ying of integers(2) is ideal of veal number (R) an DTrue D Fulse

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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: 1: What happens to the above if the root r has a multiplicity m?

A: It is given that, the root r is a root multiplicity m that is fx=x-rmgx where gr≠0

Q: Prove that for x≠0 the inequality ex&gt;1+x holds.

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Q: Use direct prove to prove that for any two positive numbers x and y, x+y Vxy s 2

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Q: Prove that 1/ r + 1/ r2 + 1/ r3 + . . . = 1/ r−1 , for ∣r∣ &gt; 1.

A: Consider, It is a geometric series with,

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

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Q: Consider the set S = {r E Q : r² < 2}. In the land of rationale numbers is there a least upper bound…

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Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: @[V2]is Principal Ideal Domain. O True O False

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Q: Q[V2]is Principal Ideal Domain. O True False

A: We have to solve given problem:

Q: Suppose x,y and z are positive real numbers. Prove that x+z/y+z>xy if and only if x<y.

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Q: To prove that dx In /1+ (In x)² + In x + C x/1+ (In x)2 we use the substitutions

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Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

Q: Show that f: R → R defined as f(a) = 3a³- 4 is a one to one %3D iuicuon.

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Q: 3. Prove that Re(2-+z')<4 when z<1.

A: a.          x+y ≤x + y                                             (triangle inequality)b. Re(z1+z2)…

Q: there exists a real number s>0 such that |2x-5|<.01 wherenever |x-2.5|<s

A: We can prove that there exists S such that given condition holds. Actually we find a particular…

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Q: Find the rank and nullity of the 2. 4 9. A z -7 2. -5 4 L7 -9 2 -4 verify the that dimension…

A: The given matrix is  A=20464-7201-5247-92-4 According to dimension theorem for any matrix A of size…

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

A: Let  z = a+ib

Q: Using R, use antithetic variables to estimate the following: In(1+ x2) dt x2

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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: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: Let r E Rt. Prove that if z – 2x2 +2 2021. -

A: Let x2=t, Now if x∈R+⇒t∈R+ ⇒t2-2t+2≤0⇒t-12+1≤0⇒t-12≤-1which is not possible for any value of t, for…

Q: (c) Prove that 10 is not separable.

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Q: Prove that the number V7 lies between 1 and 2.

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Q: Prove that R (D-1 and R)%=(-)

A: The objective is to prove that  Pn1=1Pn-1=-1n

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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: Use the IVT to find an interval of length 0.3 that contains a root of In r = 3 – 2r.

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Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

Q: 4. Verify thatf (x) = x³ – x2 – 20x + 6 satisfies the three conditions of Rolle's Theorem on [0,5].…

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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: 1. Use substitution technique to show that ++x+2+x- v2 +C dr 1 In rV+r+2 +x+2+r+ V2

A: As per our guidelines we are supposed to answer only one question that is the first question. For…