a) As x → 0, 9x-5 → b) As x → -o, -7x' + 10 → c) As x → 00, 5x-3 → d) As x → ∞, 7x

Q: Use mathematical Inductlon to prove that for r>0 and any positive Integer

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Q: - а, ь, с € R CER polynor = x° + ax

A: f(x)=x3 +ax2 +bx+c0=-23 +4a-b+c0=-8+4a-2b+c4a-2b+c=8

Q: If (0,1) ~ (-1,1) and (-1,1) ~ R. Deduce that (0,1) ~R

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Q: Without using any theorems from the book, prove the following statement: The sum of any two odd…

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Q: () = 2 sec(a O conon1 O pton 2

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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: 2. Show that In (- - ) = ( + 2nn)i where n = | .... .... ..

A: Consider the following expression: x=ln-12-32iex=-12-32icosx+isinx=-12-32i

Q: 2"-1 for positive integers n.

A:

Q: -, first prove that )" 6.

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Q: b)Show that, 6(z, 3zy – y' and (z,y) = -+3ry are harmonie

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Q: Integrate  sinnuelog(cosu) . Where n=744

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Q: he binary operation * defined on Z by x * y = 1 - 2xy. Does * satisfy commutativity and…

A: The binary operation * defined on Z by x * y = 1 - 2xy.To find does * satisfy commutativity and…

Q: 1> =a,-4,57is to U=2,-4,5 812.Detemmine -> onthogonal

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Q: Use Simpsons 1/3 rule to evaluate of e-x2 over the interval 0.2 to 1.5 using 6 segments ?

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: Arnold says that 25 = 3, and he uses the picture in Figure 3.30 to support his conclu- sion. What is…

A: Given that: According to Arnold reasoning:  223=45

Q: Show that |1 - (x, + x,) - (x, + x,) X,*z = (x, – ,) (x, – y2) (x2- ,)(x2 - 2) 1 -(), + x2) 1 - (y,+…

A: See the attachment

Q: 2) of Ec, 4" is convngend can we conclude that coch of these are comvergent: (4)

A: Given The sires is convergent then,

Q: Prove 2- = =4 has infinite many Solu thans ZEC.

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Q: Let x and y be non-negative reab· show that, use Proof by Contradietion X+4 2

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Q: 2. Show that 1 2 = (1 - )( - )(? y)

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Q: 23. Find de V100- tan O coton 2 Opbon 1

A: We have the given integral as ∫dx100-9x2 On solving the given integral furthermore, we get the…

Q: 2. If 0 is in QIII then 180° < 0 < 270° and must be in since

A: 180°&lt;θ&lt;270°

Q: The 4th term of an ap is zero. Prove that 25th term of the AP is three times its 11th term

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

A:

Q: see the equation as attached here

A: Solution:Given    0&lt;an≤bn and∑n=1∞an divergesTo prove:∑n=1∞bn diverges

Q: 96, a0ose -bsine =0 a'simo +baose asimo-baose Then,

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Q: According to boolean algebra x.(1 + y) =?

A: We will use the following 3 rules : (i) Distributive law : a•(b+c) = a•b + a•c  (ii) Identity law :…

Q: 2. Prove ΣΫ; = Y 3 Prono ΓΥΠ |

A: Let X be a Random variable with a Probability density function or probability mass function f(x)…

Q: 6.Use.chain.Rule.to.frind.E GV. ... 2Sin.x.Eoguy Xロサ.……4こ… ...... .......

A:

Q: 2 Prove Ccos(n (ulx)] duc)

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Q: Prove that (1-x*)у ,-ху, +р'у-0

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Q: Prove that. 2/nJn-(n+2)Jne2 + (n+yjJney --- 3. end hence deduce that. 1xJn - (nti)Jnas -…

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Q: s) Express the infinite contimod fraction [2, 1,5 quadratic irrational- as a ity.

A: We need to express the infinite continued fraction 2, 1, 5¯ as a quadratic irrationality. The…

Q: in= aRo can direetly /KT. by gomma fometion, We write Jo a Kox2 &KT 2

A: If you have any doubts in the solution please ask me  in comments i will reply you as soon as…

Q: Prove the fallowing egudion for every n,2 by hathematical enduelion. 35.6+35 6+ 35.63+ -+35.6"= 7.6"

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Q: If the mth term of an AP be 1/n .And nth term be 1/m.then show that it's (mn)th term is 1

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Q: 521 End Adi A R A-

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Q: 2 la), Pu (aw by Re currence relation

A: We have to find out P2(x) and P4(x) by recurrence relation. We know that the generating function…

Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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Q: 81: Without evaluoting, show directly * = ? satiefy 2. %3D 2 -5

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Q: Show that if ƒ′′&gt; 0 throughout an interval [a, b], then ƒ′ has at most one zero in [a, b] . What…

A: Given:

Q: coth- x = In () Q1/ Prove that

A: To prove coth-1x=(1/2)ln[(x+1)/(x-1)]

Q: 5!, called 5_______ , is the product of all positive integers from_________ down through________ .…

A: For any positive integer n, n! is the product of all the positive integers  from 1 to n. That is,…

Q: 6. Show that Autoq(Q[3], 5]) is finite.

A: To show: Autℚℚ35,53 is finite.

Q: Is f(x, y, z) = 8 In x+7 In y+5 In z homothetic? Of(x, y, z) is not homothetic Of(x, y, z) is…

A:

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: For n > 3, prove that the numbers ±5, ±52, · reduced residue system modulo 2". form a

A: A subset R of the integers is called reduced a residue system modulo n if (i) gcdr,n =1 for each r…

Q: 5. Deduce from (4) that the set {2} 2-: n = 1, 2, 3, ... is closed in R.

A: Given set  S =2 ∪2-1n  :  n=1  2,  3 , . . .

Q: (b) Show that when dist(x, y) = dist(x, –y), then x and y are onal. orthog- %3D

A: Given  dist(x,y) = ||x-y||