(a) (b) (c) (d) If P and Q are odd positive integers, we have mn ( ² ) ( ² ) = (m²). m Ⓒ) (@) = (₂) (F) () = () whenever m = n (mod P). a²m P = () whenever (a, P) = 1.

Q: A. If log(x + 2) + log(x + 1) = log(3x + 11) then x =

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

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A:

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

A:

Q: | 0 0 1 1 1 00011 0 0 0 0 1 5 (If the arithmetic for computing an entry involves huge powers, you…

A: As per bartleby guidelines we are allowed to do maximum of 3 subparts

Q: Show that m > (2). m! = (2″ − 1)(2″ − 2) (2¹ – 2²)... (2¹ — 2n-1). -

A: The given problem is to show the following condition m> nC2 for the given inequality.

Q: Find a number x such that x + 1 / x − 2 = 3x

A: The expression could be x+1x-2=3x or x+1x-2=3x. If the expression is x+1x-2=3x, then…

Q: Select the function that is not (n²).

A: The Big Omega () notation represents the lower bound of the time complexity of an algorithm. An…

Q: If n(Ax B) = 620 and n(B) = 31, find n(A). n(A)= n(B)= @)(::;:233)5

A:

Q: X4 none of these X (c) f'(x) does not exist.

A: f''(x) = 0  at sharp corner f'(x) does not exist for f'(x) = 0 , tangent line is horizontal

Q: (-1)^ xIn lIt) = (-1)" (n+ 2 2n+1(n + 1) che exact value of

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Q: 17. Let P1.Pn be positive real numbers such that P1+ + Pn=1. (a) Prove the following: @P² ≥ (ii)…

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Q: Given that ∑∞n=1 (1/n2) = π2/6, find ∑∞n=1    (4/n2)

A: Answer and explanation is given below....

Q: Write a in the form a=a+T+aNN at the given value of t without finding T and N. 4 r(t) = (41²) ₁ +…

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Q: 3 2 1 Let u [-]--[-]-[] -3 V 2 and w= 1 0 -1 4 (a) Show that B = {u, v, w} is an orthogonal basis.

A: The given vectors are:  u=3-30, v=22-1, w=114. (a) To show: {u,v,w} is an orthogonal basis. (b) To…

Q: Q9. (a) (i) Calculate (2 + i√5)(√5 - i). (ii) Hence verify that (√5 - i) is a root of the equ

A: (a) The given expression is 2+i55-i Multiply the terms in the given expression…

Q: Suppose P(Xi=1)=pi=1-P(Xi=0),  i=1,2 if p1> p2 show that X1>( greater than equal to (st)) X2

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Q: Q1. Solve the Following. i) (367)9 + (715)9 = ( ?)9 ii) (715)8 - (367)8 = ( ?)8 iii) (296)12 +…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find fo go h. f(x) = x − 1, g(x) = √√√x, h(x) = x - 1

A: Given that: We have to find the value of .

Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

A:

Q: N1/2 (x) = -J_1/2(x) الخيار 4 J1/2(x) الخيار 3 J-1/2(x)

A: The equation that describes the relation between the Bessel's function: Jvx and the Neumann's…

Q: Show that (an) is increasing

A:

Q: Which of the following statement is always false? (a) For all integer x, [x] = [-x] (b) For all odd…

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Q: Let f(x) 273 find f(") (x). O a. (-1)"(2+2)! 4743 O b. (-1)" '(2+2)! 4013 O c. (-1)" (2- 2)! O d…

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Q: 6. (a) Use convolution to find the inverse of the following. You can leave your answer as an…

A: (.)   Given ,            (.) Convolution theorem:  Let  ,  be two functions such that , then ,…

Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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Q: (a) Find the left cosets of {e, (1, 2)} in S3. (b) Find the right cosets of {e, (1, 2)} in S3.

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Q: a) Let p=13. Compute L2(3) b) Show that L2(11) = 7.

A: Here concept of field is used.

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given: m divides nWe need to show that GFpn:GFpm=nm

Q: If m divides n, show that [GF(pn):GF( pm)] = n/m.

A: Given : m divides n . To prove : GFpn:GFpm=nm.