3 We can de fine the fallaing tunction on real mumbers ( called "absohite value") ; abs (x) = x if xZ0, and abs (x)=-X if x

Q: Let C1 : y = x² sin 3x, C2 : y = x2 and C3 : y = -a², then (1) C1 touches C2 at infinite points (2)…

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Q: (a) Show that xn → x and Yn →y implies Xn + Yn → x + y and also show that an -→ a and Xn → ax. → x…

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Q: If the function (x) =sin 2(2n+1)x for some positive integer number n, then the conclusion of Rolle's…

A: Given that: f(x)=sin2(2n+1)x on the interval π8, 3π8.and satisfies the Rolle's theorem at…

Q: 1. Let x, y, and z be real numbers. Prove the following: [a] -(-x)- x [b] (-x )y = -(vy) and (-xX-…

A: Given x is a real number such that x≠0 To prove x2>0

Q: 9b of sido s8 Into4 gnggit EGcops otivostnsliM If ((h IR>R such that h(x) =x-6) and (g R --63-70000R…

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Q: -145 2. find least 0అ కావులి Sంఖనాుంది spcave Axz b A z] 1 -4 1 1 2. 2. enter xas a Coloumn ve

A: Given that, AX=b A=1-4010012-1121,   b=3134 The least square solution to the system AX=b is the…

Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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Q: 26 If A = then det(A) is Zero %3D %3D -5 4 Choose Zero Nonzero Thus, A 1 and det(A 1) =

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Q: : 2 < x < 4} and B = {x € R : –4 < x < 1}. Prove

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Q: 7. There is aremovable discontinuity at x = 1 andf(1) = 4

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

A:

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

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Q: Show that \{e ^ (- x), x * e ^ (- x)\} is a fundamental set of solutions of y^ prime prime +2y^…

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Q: 6-8(/2) Ce?: x3+2°<9, x<0?\ ): ト 4,X,c03 and 年(カx2)= (4),6) = (-2x2 , 3w×2) ncludng Sfidx + dr2 = ST…

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Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

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Q: 4. Find all values of x satisfying In[(2x + 1)(x +2)] = 2 In(x+2). Verify the values of x you found…

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Q: (8) Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if…

A: (8) To Find: Infimum, minimum, supremum, and maximum of the given sets S: 1. S=1-1n| n∈ℕ 2. S=x∈ℝ |…

Q: (8) Find the infimum, minimum, maximum and supremum of each of the following sets (write d.n.e. if…

A:

Q: Suppose that y' = f(y) has no constant solutions, where f : R -> R is infinitely many times…

A: Consider the provided question,

Q: HW4| Prove How 4 Prove if x;→ × then 6x.→6x Xj ->

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ² = 4. Maximize Q = 4xy, where x and y are positive numbers such that x+y %3D y: (Type an exact…

A: topic - application of derivatives

Q: 6. Show that the half open interval [0, 2) is uncountable. (Hint: We know that (0, 2) is uncount-…

A: Since the interval (0, 2) contains the infinite subset {1.2,1.3,1.4,...} So (0, 2) is either…

Q: The Wronskian of a fundamental set of solutions of the DE 2y (10) + y (9) - y=0 is given by 6. O…

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Q: Define injections f : N → N and g : N → N by f(n) = 2n and g(n) = 2n. From f and g, the…

A: Given  f:N→N and g:N→N are two injective function defined by f(n)=2n and g(n)=2n Let 2n = k then…

Q: 13. Which of the following quartic fun tions has x =-1 and x =-3 as its only two real zeros? Oy=x-…

A: If -1 and -3 is zero of function then at -1 and -3 value of function must be 0

Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 125, and…

A:

Q: 1. Show that for all z1, Z2 E C, Then we have: |Z1 + z2| < ]z1]+ |z2| 2. Show that for all z1, Z2 E…

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Q: 3. (a) How many non-negative integer solutions (x1, x2, x3, x4, x5) are there in each of the…

A: As per the guideline, 3 subparts can be answered. please repost the remaining subparts. thank you.

Q: Compute the convolution x[n]*h[n] for all n> 0, by using Graphical or Tabular method. x[0] = 3, x[1]…

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Q: Find three positive integers x, y, and z that satisfy the given conditions. The product is 8, and…

A: Use Lagrange method to solve

Q: The expansion 1 + x + x² ... approximates (1 - x)1 if O x is not equal to 1 本 O absolute value of x…

A: The expansion 1+x+x2+.........approximtes 1-x-1

Q: If g(y) is differentiable for 2<_y<_3 (<_ means less than or equal) and g(2) =g(3)=-1, then there is…

A: There is one theorem i.e. Rolle's theorem states that if a function f is continuous on the closed…

Q: 3. Let f = ax² + bx + c, for a, b, c real numbers and a ± 0. Prove that f is a prime in R[x] if and…

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Q: 4) Consider the function fex)= Slx-s] Evaluate 7-4 for any There is no solution to the equati on…

A: Given: fx=5x-5 so, f7-f47-4=57-5-54-57-4=52-13=513=53

Q: 3 and for n > 2, an = 2an-1+5, express an in terms of n. 1. Let, a1

A: The solution is given as

Q: 4.By applying the Convolution Theorem to calculate L-1 is obtained: Determine the value of (a+b): a…

A: We have to find the solution.

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

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Q: 1. For positive integers i, j,n such that i+ j = n (a) show that corresponding multinomial…

A: sol(a) we know that multinomial co-efficient is definedby ni,j=n!i!,j!  —(1) where i+j=nnow…

Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: 3 Prove that Var(aX– b) = a² Var(X) where a and b are constants. %3D |

A: We know that the V(X) =E(X2) -(E(X))2 By using the  above definition of V(X), we can easily prove…

Q: 6. Inductively prove that B(0) = 0 for all n. Conclude that B(2) is C° function. %3D a

A: We prove the above theorem by induction. We have to prove that Bn0=0 ,∀n...1 Take n=0 then, Bn0=B0=0…

Q: The Wronskian of a fundamental set of solutions of the DE 2y (10) +-y (9) -y=0is given by O None of…

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Q: 5. Determine the Wronskian of the functions (x)=x2 and g(x)=3x2. For what values of x is the…

A: Please refer to the image below

Q: 4. Prove that n(3n – 1)r x + 4x + 7x + ... + (3п - 2)x for n e N.

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Q: Which of the following conditions is sufficient to guarantee that integers x, y, and z satisfy the…

A: x(x-y)+y(y-z)+z(z-x)=1 Put all the given conditions and check which one is valid.