Show that conversely the given relaution implies that n Ly.show that this may not hold If x is complex.give examples.

Q: Proof Assume that 2 | (x² − 1). So x² − 1 = 2y for some integer y. Thus, x² = 2y + 1 is an odd…

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Q: 2. Let f(x) = x - 5 and g(x) = x² +3x. a) Find (f + g)(x) b) Find (f – g)(x) c) Find (f g)(x) d)…

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Q: f(x)= 1 √1-x 寫 款

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: tan (w+2n eくな foo ttait

A: We have to find value of a and b :

Q: if f and g have a pole at zo and both have nonzero residue then fg has a pole at zo with a nonzero…

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Q: a. Give the smallest extension of Q that contains all the zeros of x4 - 2x2 – 15.

A: We shall answer first question only as you have asked diff question without mentioning. For others…

Q: Find the subdifferential of the following funtion: f(x) = |c' x|, x E R“

A: given clear explanation below

Q: Sp

A: The question is asking to verify the statement that for all real numbers x and y, the product xy is…

Q: best Rank 2 approximation F ind weth respect to I|F|l the where to A -1 2 -1

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Q: Show that: 8 [J₁(bt) t" eat dt ed 0 2"b" I(n+-) 2 n+- 2 √√π (a² + b²) T

A: To prove the given integral identity, we will use the integral representation of the Bessel function…

Q: 2 X+2| dx -3

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Q: INSTRUCTION: Prove or disprove 1. Show that f: R-{-}→ R-{} defined by f(x) 3x-5 = is bijective. 2x+1

A: Given :  f: ℝ--12→ℝ-32   defined by ;                f(x) = 3x-52x+1 To prove : f is bijective.

Q: Which of the following are indeterminate forms e. sot co b, d. h. Ox 0∞ ; ox O 9. ∞-00 8/8

A: To identify the indeterminate form from given data

Q: if it was Nlo11). Prove that F(2) = 1-F(2)

A: Step 1:We know,  F(z)=2π​1​∫−∞z​e2−t2​dt, so F(−z)=2π​1​∫−∞−z​e2−t2​dt. Step 2: By using the…

Q: PLEASE TYPE ONLY*** Exercise 4.2.3: Find a counterexample. Find a counterexample to show that each…

A: we have to write the counterexample to show that the following statements are false

Q: Assume that u x =. Use the properties of the cross-product to evaluate the following expression.…

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Q: Evaluate the following complex functions and show your complete solution

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Q: (i) (z+ yx)(x+ yx)(xy+xZ)(z+y)

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Q: 5. Find Wxxyyz, Wzyx, and მაw Əzəx²ǝy² if w(x, y, z) = x³y-5 + sin(xyz) + In(x + yz). C

A: Note: All partial derivatives are not small. I can solve only first two partial derivatives as no…

Q: Discrete Math 2.4.3. Prove each of the following algebraic statements using a direct proof: a) For…

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Q: (2) The real part of Syy (@) and the real part of Syx (@) are even functions of o, i.e., Re[Sy (@)]…

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

A: Given that, The set A has Infimum 2.  B={x∈R|∃a∈A, x=3a} We have to show that B has infimum 6.

Q: Q6. Use Taylor's Theorem to prove that if x > 0 then, 5 1+

A: Given,x>0 To prove: 1+x12-1+x3+x29≤58!x3

Q: Verify the statement is incorrect by giving a counterexample. X is greater than and equal to 5

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Q: 2. Prove that fo So dx=3(2-√2)

A: We need to solve integration problem.

Q: FOR THE FUcnoH Xe*, FIHN THE MACLAURI SEAIES APPROXIMA TIOU

A: Given:

Q: Sp

A: The question is asking if the product of two real numbers x and y, represented as 'xy', is equal to…

Q: If possible make an explicit bijection from [0, 1] to [-2, -∞. If no possible, Why? If…

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Q: Express the following complex-valued Jundion zGt) = uGt)+ ivGt), where uCt) and CH) are real-valued…

A: Z(t) =(2-3i)cos(2t)-i sin(2t)  Or Z= 2cos(2t)-3icos(2t) -isin(2t)  Or Z= 2cos(2t)…

Q: Let z be a root of z5 – 1 = 0 with z # 1. Compute %3D 215 + 216 + z17 +· . + z50

A: Since z is a root of z5-1=0 ⇒z-11+z+z2+z3+z4=0⇒1+z+z2+z3+z4=0…

Q: Explain why you know that λ is a root of charL(x) if and only if Ker(λId-L)≠0

A: To prove the equivalent conditions on the roots of the characteristic polynomial and the kernel of…

Q: Simplify (x + 3)(x+ 6).

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Q: determine if the functions are one to one y = √36-x², y = = = ² 2 y =√x+1 − 3 1

A: A mapping f: A→B is said to be one-one if for each pair of of distinct element of A, their f are…

Q: Consider the subring S = 2216 of Z16. Then char (S) = 4 6. 8. оОО О

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Q: 5a. Prove that cosz is an even function, but tanz and cotz are odd.

A: Let, f(z) = cos z     Now, f(-z) = cos(-z)                        = cos z = f(z)  So, f(z) = cos z…

Q: the P to values what tot below A.

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