for A(x) on [0, 2] and (2, 4]. ers in exact form. Use symbolic notation and fractions where needed.) x) =

Q: Show that for A symmetric inf. = Amin(A).

A:

Q: Show that (n+1)Pn+1(x) = (2n + 1)xp,(x) – npr-1(x) ;n> 1? %3D

A:

Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: 6. Show that, for integer s, S. s! | x25+lexp(-ax²)dx =: 2a +1

A: Note: Given proof statement has a little mistake, I have proof the actual result. First i have…

Q: If y = exp(-x²) show that -2xy and hence prove that, for n > 1, %3D y(n+1) + 2xy(") + 2ny("-1) = 0.…

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Q: Express In V16 in terms of In 2 and/or In In 16 =[ (Type an exact answer.)

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Q: f(x)=2sin(x)+4cos(x), then f'(x)=? f'(5)=?

A: Given  f(x)=2sin(x)+4cos(x)

Q: Find the product and addition of the approximate numbers x, = 32.452 and x, = 24.3595 all of whose…

A: x1=32.452 and x2=24.3595 To Find: a) Product and addition of the approximate numbers. b) Relative…

Q: Suppose you are given four natural numbers w, x, y,z e N such that w>x and y > z. Show that ly – w|…

A: It is given that w, x, y, z are natural numbers such that w>x and y>z. Now we want to show…

Q: ZA is complementary to ZB and ZB is 8. Suppose

A: If two angles are complementary then they makes to 90°. If two angles are supplementary then they…

Q: If (ar + br) = 2n %3! n+1 and k-1 8. E(ak - br) = n+2 - , then ar %3D k-1 k-1

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Q: It x~N(μ,σ"), then ²~. Option 2 ption 1 *** *** *** N(0, 1) G(1⁄2,2) x² (2)

A: Given, if x~Nμ,σ2 Then x-μσ2

Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

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Q: of Voots of the equation. 2x+3X+5=0 is The muttiple is Ę 2. 3 Prove That The sum

A: Use the formula for the sum and product of the roots of a quadratic equation.

Q: Q.2) Evaluate cln 7 cln 2 cln 5 e(z+y+3) dzdydr In 6 In 4

A: Given triple integral is ∫ln6 ln7∫0ln2∫ln4ln5 ex+y+z dz dy dx   Note:- ex+y+z =ex ey ez

Q: Pebermine x and such that -4 3 -4 -4 -3 4 -8 4 -4 -2 3. 3. OC

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Q: 2. Find p and q such that |5x - 2| ≤4 implies Ps 23x-4 5 ≤q.

A: Given |5x-2|≤4

Q: for n>2, 5 . Deermine for whpch n, n2-2 let |anlく,

A: Given  an = 5nn2-2

Q: Indicate the method you would use to prove the two A's . If no method applies, enter "none". of

A: Given ,  Here ,  Two angles are equal and one side is equal .

Q: for intergers a and b, the fraction a/b is in reduced form if and only if GCD(a,b)=1 True or False?

A: The given statement is true because this is how the reduced form of a fraction is defined.

Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

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Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: In ALMN, LN is extended through point N to point O, m/NLM = (x – 4)°, mZMNO = (4x – 17)°, and m/LMN…

A:

Q: GIVEN: 2x - 3 = 7 PROVE: x = 5

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Q: 3. Find the deriotive of the Ronclion VE t6

A: to find the derivative of the following functionh(t)=tt+6

Q: in tions Practice - Add Su 3. 3D 5.

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Q: 5x 60(x, +x,) 3 b) Y = In 60(x2 . 3,

A: The given differential equation:                                                 Y=ln5x1360(x2+x1)32…

Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x>0 we have to prove that…

Q: FOR N=195, by fermat's theorem an-2 =

A: Given: FOR N=195, by Fermat's theorem an-2

Q: Suppose X~N(112,16), and Z~N(0,1). Then x = 112, is equivalent to z = ______.

A:

Q: 2/Given frx)= 3Xtl a evaluate (flof(s) 1-SUEJECT NOTEBOOR 9. fo

A: Topic:-  function

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: Prove that tanodo-n//2.

A:

Q: 5. For non-negative integer n and r, where 1<rsn, show that (n-r+1)"C,1=n(""C,). r-1

A: Given n and r non negative integers with  1≤ r≤ n. We need to prove (n-r+1)nCr-1=n(n-1Cr-1)

Q: es lls ew zeiflucifiib ons einiseen stigesber Show that for neN, (2n)! ' (r!)² ((n −r)!)² - 7=0 2n -…

A: We will use binomial expansion to prove given relation

Q: Given: 5(2x – 8) = 30; Prove: x = 7 -

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Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: 4. Show that if ki = (X; - X)/[Σ(X; – X)2], then (a) Σki = 0; = (b) Σk? = 1/[Σ(X; − x)2]; (c) Σκ;(X;…

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Q: What are the value for sup e-* = е x>0 and inf e * - = XER

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Q: ) Evaluate, using Cauchy formula C:2- (a) zz-l dz dz (6) ( e

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Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: Q3- Give an example of two denes not equal X subsets of (R,Te) and (z,ror ). ( Explain your answer…

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Q: Show that yn Z, if n³+5 is odd then n is even

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Q: How do I subsitute X= Ztan into Ha):" ) How do I simphtiy asuming Ok Be

A: Solution : We have given a function fx = x4 + x2   To find : Substitute x = 2 tanθ into the given…