Prove the inequality V1+æ – 1 –+ < 6 on [0, 0). 8

Q: Solve the following inequality graphically in two-dimensional plane:y &lt; – 2

A: We first draw y=-2 line

Q: Evaluate the sum of with x1 = 0, x2= 2, x3 = 4, x4 = 6, and Ax= 1, for f(x) = 5x -2. i=1 4. i=1

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Q: Solve the following inequality graphically in two-dimensional plane:2x – 3y &gt; 6

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Q: Prove that the set S = {n² : n e N} is denumerable. %3D

A: We have to show that the given set S is a denumerable set.

Q: STION 16 implify the inequality z² + 2z < 15.

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Q: 1 Find the absolute maxima and minuma x²-2x4+ bunded by y= x², y=t, the closed negion on %3D…

A: Given that, f(x,y)=x2-2xy+y Take the derivative for x, fx=2x-2y Take the derivative for y, fy=-2x+1…

Q: Prove that for all integers n > 2, f(x) = x/n is continuous on [0, 0).

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Q: n! Prove that the maximum value of when n. +n2 t+ nr =n n.! n.! na! ... is given by n, = na = = ny =

A: The expression n!n1!n2!...nr! will be number of different permutations of n objects with n1, n2...nr…

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x € R: 1/x e A}. 1…

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Q: Prove by mathematical induction: X n (U-, Y) = U=1(X nY), for V n E Z* – {1} and sets X,Y,,Y2,. Yp-…

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Q: R is the amount of rain, in inches, on any particular day in 2012, and it is said to be uniform…

A: Wr want to find the probability by chebycheves inequality.

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/xe A}. 1…

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Q: 2. Let f : (0, –→R such that f(x) = x². Show that f(x) < r. • Show that f has no fixed point on (0,…

A: The given function is f:(0,13]→R and defined as f(x)=x2 . we have to show that f has no fixed point…

Q: Prove using the IVT. 2x = bx has a solution if b &gt; 2.

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Q: If T4O isa bounded Linear ope rator. show that Forany XEDCT) such that llx ||<1 we have the strict…

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Q: Which inequality describes the restrictions on x according to the hinge theorem? 5x 95 5x + 3 3x+17…

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Q: In(2) ith(7-32) + vr² + 1. Answer using interval 3. Find the domain of the function f(x) = + In…

A: In our function three expression added together. Hence we going to see each expression separately…

Q: 3.19 Suppose if r = 0, f(x) = {-1)" if r E n+1' n where n E N. Prove: f € R[0, 1], even though f has…

A: Sol

Q: (c) Let z1 = 2+ 2i and let 22 =1+i. Prove that the triangle inequality |21 + z2| < |21| + |22|…

A: Left hand side is equal to, z1+z2=2+2i+1+i=3+3i=32+32=32 Right hand side is equal to,…

Q: Let X ~ N(0, 1). For any € > 0, show that P(|X| > c) ≤ ²c - ??

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Show that the function f(z) = from [0, 0) to [0, ∞) has a fixed point c. Hint: Set f(r) = z and show…

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Q: Use d'Alembert's solution to prove f(-3) = f(3),g(-7) = g(3) for the semi-infinite string satisfying…

A: Now, it is given that ux(0, t) = 0   The D-Alembert’s formula is given as:

Q: 1 Show that n2 + 1 IN V

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Q: Find all values of m such that a(r) = {X – 1 if x m is continuous everywhere.

A: Questions from real analysis.

Q: 23. Let A be a non-empty set of positive numbers, which is bounded above and let B = {xe R: 1/xe A}.…

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Q: 12) Show that D- d-del is shortest distance betueen a x- by +c2.of ; and ax+by tcz= dz?

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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: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

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Q: Prove the following inequality. Do not evaluate the integral. 1 ,1 - x² + x +1 | - 2 0, 1+ x4 4

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Q: (a) Determine whether all of the hypotheses of Rolle's Theorem are satisfied on the stated interval…

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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: 2|A:k||2|| Bx:||2) < || |||B||F k%3D1

A: Please check the answer in next step

Q: Let A be a non-empty set of positive numbers, which is bounded above and let B = {x e R: 1/x e A}. 1…

A: Remark: Completeness property of R: Every bounded above non-empty subset of R has a least upper…

Q: 9:Find the absolute exlemum Verlues of flx) x²-4x+24 over the interNal Cl,41

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Q: 5. Find all pairs (m, n) of positive integers such that y(y(nm)) = n, where p is Euler's totient…

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Q: Verify that f(x)=x2+1/x satisfies the hypotheses of the Rolle's Theorem on the interval [1/2 2] and…

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Q: Show that the f(x)=x-(In x)^{x} =0, has at least one solution in the interval [4, 5]. O f(4)=0.31,…

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Q: Show that the IVP x" = –6x(x')3, x(-1) = -1, x'(-1) = 1/3, has a unique solution x and find the…

A: The given initial value problem is, x''=-6x(x')3                                     ..............1…

Q: - Use the Exterior Angle Inequality to find an upper and lower bound for LMLK = y. %3D M 70° 50 K L.

A: Given: To Find: The upper and lower bound for ∠MLK=y° using exterior angle inequality

Q: find the root of the fnmetion ーX FCx)= ē^ _ x which lies betwen (o %3D

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Q: For p = (1, 0) and x = (x₁,x2,...,xn) ER", define ||2|p:= - ². |P Show that n jyjx|py|q for x, y…

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Q: Solve the following inequality graphically in two-dimensional plane:y + 8 ≥ 2x

A: Given:

Q: Solve the following inequality graphically in two-dimensional plane:3x + 4y ≤ 12

A: We first graph 3x+4y=12 line We make a table for it x 4 0 y 0 3

Q: -) verify that the function Satisfies the three hypotheses of Rolle's theorem on the given interval.…

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Q: Solve the following inequality graphically in two-dimensional plane:– 3x + 2y ≥ – 6

A: We first sketch – 3x + 2y = – 6 line We will use a table for this x 0 2 y -3 0

Q: 5654 12 O E 2x V x + 5 Applying the Hinge Theorem, what inequality can give the correct restriction…

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Q: Use the mean value theorem to establish the following inequalities: x-1 b) 1 -

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Q: Let S be some non-empty collection of real numbers. We know that Vx E S, 3y E S such that x2 y.…

A: In this type of question you need to assume the set of x,y and S that satisfy the condition given in…

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

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Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n