Prove using the IVT. For all integers n, sinnx = cos x for some x ϵ [0, π].

Q: For each n ≥ 1, take An= (-1/n, 1/n). Then, 1 An {0} and U1 An (-1, 1). Prove these.

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Q: Calculate the upper and lower bounds: 4+cos c/3+sin c  c∈R

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Q: Let Sy := {1-(-1):NEN. Find iNf Sy and sup Sy

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Q: Let y1, . ... Yn real numbers, and let n y = 1/√ Σ² ²=1 Yi n their arithmetic mean. Show that for…

A: The proof is explained in the explanation section.Explanation:Solution: Let's prove the given…

Q: Suppose that z is a function of z and y and that ze y cos z. Find and

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Q: Evaluate a x cos(ry) dA where R = [0, 7] ×x [1, 2]. R

A: we have to evaluate the following integral

Q: Find Pr (|w| < 0.2)  where W ~ N (-1,4)

A: From the given information, W follows normal distribution with mean µ=-1 and variance σ2=4.

Q: Let s = {x €N : 2 < x < 9} and T = {x eN : 5 s x < 14}. Then snT = {x €N : 5s x < 9}. Select one: O…

A: We have to choose the correct option.

Q: erify that they satisfy al ar argument sin(m - 1

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Q: 2.Expand the following in powers of x i)√(1 + sinx) ii)e cosx iii) cos x²+

A: Given data:- (i); 1+sinx (ii); excosx (iii); cos-1x2-1x2+1

Q: 4. Find an upper and a lower bound for the set E= x +1 : -1 < x2 +1

A: Given: E=x+1x2+1:-1&lt;x≤2

Q: Show that — ф+1 n=0 ||

A: Given φ is the golden ration satisfying 1φ=φ-1. To prove ∑n=0∞1φn=φ+1 It is known that φ=1+52.

Q: f T is nilpotent of index k. Show that Tn , n>1 is nilpotent  of index k.

A: we have that T is a nilpotent matrix with index k. And our claim is to show that index of matrix Tn…

Q: IRI- 2. <| sinz|< -e 2

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Q: Find the singular values σ₁ ≥ σ2 of 01 = 02 -1 -27 A = -2 1 -2 2 9.

A: Find the singular values σ₁ ≥ σ₂ of the matrix A: Singular values of a matrix are the square roots…

Q: Suppose x is a fixed real number. Show that the following hold. (Here y is a real variable.) lim y→∞…

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Q: Q5: Show that S 2T Cos 30 5-4 cose 11 ㅠ 12

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Q: Which of the following are not solutions of 3 tan(x) = √3 over the interval [0, 2ㅠ)? Check all that…

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

A: To show: Autℚℚ35,53 is finite.