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Q: get an 6Usc Thesrmn to show that -x gra) = 2 has a unique haed %3D point on

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: f(x) = sin nx OKKI, > n such that If exist KEIN If₁a) - foxil < 10 Ans. K =11 / does there K and XE…

A: The given function is fnx=sin nxn, 0≤x≤1 To find: the value of k.

Q: 73. Use De Moivre's theorem to show that 2( cos + isin 9. is a cube root of 8 cos 9 + isin- 3

A: De Moivre’s theorem is (cosθ+isinθ)p=cospθ+isinθ We have to prove that:…

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Q: Prove that (23-1a,b)* = {2}-1/a})(27-1) j=1 for all real numbers a₁,..., an and b₁,..., bn. i=1

A: The detailed process is described in step 2.

Q: SP, (cose) cos no de Pn = B (n + 1, ¹), n€ N.

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Q: b) Find the inverse ztransform of the following: i z's zl2|sin 3 2(2/2/cos 3)z+|2/F] zz(z*+4z+1) 1…

A: We will use the basic knowledge of the theory of z-transforms to answer all the three subparts of…

Q: How 3 used a (aluchy - Schwarz invquality Fuclideran distance. the to show that matric on R"

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Q: find the denivahon of the Runchon bydsing herules ofditkreohe lhon fee) = 7 %3D +260 .3 2.

A: We need to find the derivative of given function. fx=7x3-8x2-1x+250

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Q: 2. : (a) For n ≥ 1, show that 1+z+2²+...+ 2¹: (b) Hence, show that 1+ cos 0 + cos 20 + 12+1 2 #1 7…

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Q: cos" xdx :0. 6. If n is a positive odd integer, prove that

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Q: Steb by step

A: We will need integration by parts for this problem. So we assume u and dv and from there find du and…

Q: Find the efeneral Solutim Of the differential equatim: (0?-40+3)y=x+ee+x?

A: Answer and explanation is given below...

Q: Given that x>0 and y>0 proof that xy>0. (x,y are integers)

A: Given that x&gt;0 and y&gt;0, then to prove that xy&gt;0. x, y are integers.

Q: S 0 ecos sin 20 de

A: Topic - Definite integral we are given ∫0πecos θsin 2θ dθand we know that∫exdx=ex+Cand integration…

Q: FOo=X-1 de fined 2n E- lro] show that Fis Riemenn integruhk

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Q: c) Let k EN be odd, show that (1+i)2k + (1 – i)2k = 0 d) Using Demoivre's theorem, show that, if z =…

A: This Question Contains the multiple part.  For (b) we will use the principal of…

Q: Which of these is a possible solution for sin²x - 1/1/72 = x = [0, 2π] ? a) O b) X = x = Oc) ₂ 元_4 П…

A: Given:      sin2x-12=0        sin2x=12         sinx=±12        sinx=12 , sinx=-12

Q: What is the tangent of 0? 6 D 6V11 11

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Q: gg Un= 0 1- Cos nn dr 1- Cosit Unt₂ + Un = 20 ot prove that

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Q: ) Let Z= re q iy be a complex mumber Such that cosh Z+o. then Re (tanh z) is equal to Sin a cesn

A: In the given question we have to find the real part of tanhz and and also check it that is it equal…

Q: 13. Write sin(tan-)) ; x > 0, as an algebraic expression of r. 49 + x² iv) 7 ii) 49 + x² iii) 49 +…

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Q: How to formula asin BØ + bcos BO а √a²+ b² cos (BO-C) Where C= arctan (a/b) C = arc tan (a/b), a>0…

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Q: (−1)” - {1- (-²; n = N / is n The supremum of the set S=1- a) 1 b) 0 c) n d) 2

A: We haveWe have to find the supremum of the set S.

Q: (q) {0,1,2, 4, 8, 16} (s) s) {÷ :n E N and n is prime} (u) {x² : x € R} (w) {sin(): n E N} n 3

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Q: -3 < x To nenen Is fox is odd ? even or

A: Use definition of odd and even .