Given 2822. Identify the postulate or theorem that proves that r || s.

Q: Q3 Prove that In Coth x 1

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Q: 10 Sx³ex¹⁰dx= (Type an exact answer.)

A: Given integral is as follows

Q: |a|, called the of a, represents the distance from on the number line. to

A: It is known that a represents the absolute value if a.

Q: Let Z∼N(0,1). Find P(-2<Z<1).

A: From the provided information,Z~N (0, 1)The probability P (-2&lt;Z&lt;1) need to be calculated.

Q: Determine if 0 >=(61-6-J-RA) is in the span of = 0

A: Given: -1225 To check:If -1225 is in the span of Φ=1100, 1001, 0110, 0011 or not.

Q: Suppose the set of natural numbers is constructed by the constant 0 and the successor function s.…

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Q: 5. Let F= [3,2,1] and r= [2,1,–3]. Compute the following: %3D a) Proj „F. b) Orth rF = F – Proj „F.…

A: We know that  ProjrF=r.F∥r∥2r Now, r.F=23+12-31=5 ∥r∥2=r,r        =2,1,-3,2,1,-3        =22+11-3-3…

Q: (2) For each nEN, set D= [ Find each of the following (2) U Dn. (b)

A: Given Dn = -7n, 5n

Q: .18 Let x, a and 8 be real numbers. Show that the statements |x-al < 8 and a -8 < x < a +8 are…

A:

Q: Evaluate the following commutators [Â, B] = ÂB – BÂ. Hint: use an arbitrary function that cancels at…

A: a x,PxPx=-ih∂∂xx,Pxφ=x,-ih∂∂xφ=-ihx∂φ∂x+ih∂∂xxφ=-ihx∂φ∂x+ih∂φ∂x+ihφ=ihφ∴x,Px=ih

Q: Show that if a|m and a|(ms+nt) for some integers a≠0, m, s, n, and t, then a|nt.

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Q: Let S, be the set of real numbers such that their decimal ex- pansion contains 3 at l-th place after…

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Q: h9HXth*x f3.1) he mt itextsS St ,2)

A: Given:

Q: If z1:2., are complex numbers such that =|= =. = |=,| =1, Prove that

A: To prove: z1+z2+…+zn=1z1+1z2+…+1zn Given: z1=z2=…=zn=1 Since, (1) zz¯=|z|2 (2) z=z¯

Q: Let a1, a2, ...,a, be real numbers that are all contained in the interval [-7/2, 7/2]. Use the…

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Q: 3. Let r be a real number. Prove by contrapositive that if r+4x <35, then z < 3.

A: Note: Proof by contrapositive: If we want to prove that "if A, then B". Then we use contrapositive…

Q: Prove the following:  If a <b, then -b < -a

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Q: Prove Proposition 3.4. A monotone function that is defined on an interval is measurable.

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Q: Suppose that x is a real number and that UCR. Prove that the following two conditions are…

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Q: Show that ACB implies |A|≤|B|.

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Q: Write the mathematical formulas corresponding to the following statement with the help of the…

A: Given statement : Every function with positive and negative values has a root.

Q: Let x, y, z E Z be such that both odd, and z is even. Prov

A: Introduction: Even and odd numbers are distinguished by the following characteristics: Even Number:…

Q: prove for every positive real number x that 1+1/x2>=1/x+1/x3.

A: To prove: 1+1x2≥1x+1x3; for everypositive real number x.

Q: Let a be a real number. If lim, »0 47 = 8, VIta-Vā then which of the followings is the value of a?

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Q: 5 Find the least common denominator of X 11 and 4 8x+5' X 3

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Q: Q3 (Recall the notation: For any set S CR and any k eR, kS = {ks : sE S}.) (a) Someone has claimed…

A: We will use the fact that the set of integers is countable and every subset of a countable set is…

Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…

Q: 5. Function fand g are defined by formulas as shown below. f(x) = x³ and g(x) = x- 1, for all real…

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