Prove that if n> m - 1, then J,(x) = 2(x/2)"-m

Q: Determine one real root of 2xcos2x – (x – 2) = 0 cn the interval (2, 3)using the Regula-Falsi…

A: Given 2x(cos(2x)) - (x-2)2 = 0  Let f(x)=-(x-2)2 + 2x(cos(2x)

Q: e3x e(n+1)x = 1+ e" + 2 enx Sx 6. n! (n + 1)!

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Q: Suppose r is a non-negative real number and n is a natural number. Use the Binomial Theorem to prove…

A: The binomial theorem states that for the positive integer value n: x+yn=∑k=0nCknxk+yn-k

Q: Prove that _f₁ = = ₁+2 +851+1 −85₁-1 + ₁-2 +0(hª) 12h

A: Use taylor series expansion to prove this

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: 1 Q6) Let H(x):=k for x=, (k eN) and H(x):=0 elsewhere on [0,1] k Determine whether H(x) eR[0,1 or…

A: Unbounded function is not Riemann integrable.

Q: 5.3.2 (a) Suppose that n > 3. Prove that ("+1)ʻ 5.

A: Given:-             n+1n2 < 2 n+1n2 -22<0n+1n+2n+1n-2<0n+1n+2 =…

Q: Prove that 2 1 1 5 2 (4-2x)² for all relevant x-values

A: Given is a expression  1215-x>24-2x2. It is required to prove the given expression for all…

Q: If n is an even integer prove that Φ(2n) = 2Φ(n)

A: Given: n is an even integer.To prove: ϕ2n=2ϕn

Q: If n^2+6n+11 = x^2+y^2 for positive integer n, x and y prove [xy/2] is composite. Note: [t]…

A: Given :              n2+6n+11 = x2+y2              t ≤ t

Q: (4) (LATEX question) (2018A8(b)) Use the Intermediate Value Theorem to prove that for each real…

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Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: Show that /(-1)-7(1) but there is Let f(x) 1 Show that /(-1) (1) but there is no number e in (-1, 1)…

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Q: d. y= x² + y x + cos y

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Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: Prove that coth-la = In x +1 for |a| > 1 x - 1

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Q: Show that det [1 1 0 0 1 1 0 0 1 0... 0 0 1 ⠀ ... 0000 1000... 00 00 11 0 1 = 1+ (-1)"+¹.

A: As per the question we are given a matrix determinant, whose all diagonal and super-diagonal…

Q: Bruce and Cruz had 294 bookmarks altogether. Bruce gave away 3/8 of his bookmarks and Cruz gave away…

A: Let the number of bookmarks Bruce has = B The number of bookmarks Cruz has = C therefore B+C=294…

Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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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: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Prove that there exists a unique real number solution to the equationx +x² – 1 = 0 between x = 2/3…

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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: If In x + In(x – 2) = ln(7x), then x -

A: From the given problem:   lnx+lnx-2=ln7x   Now using the logarithmic property:   ln(a·b)=ln(a)+ln(b)

Q: 4cos20 + 2/3 = 0 on the interval[0, 3t]

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Q: 3. (a) Find a unit in Z[√2] which is not equal to 1 or -1. Hint: Use 1 (b). (b) (*) Show that Z[√2]…

A: The objective of the question is two-fold. First, we need to find a unit in the ring Z[sqrt(2)] that…

Q: Show that for any positive integers i and j with i > j, we have T;(x)T;(x) = [Ti+;(x) +T;-j(x)].

A: we have to show, for any positive integers i and j with i&gt;j TixTjx=12Ti+jx+Ti-jx Now, we know…

Q: (d) If each fn has fewer than M discontinuities (where M ∈ N is fixed), thenf has fewer than M…

A: To Show: If each fn has fewer than M discontinuities (where M ∈ N is fixed), then f has fewer than M…

Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: If m is a positive integer and x > 1, then show that 1-4¹ (-1)" xm+1 m! 2 F₁ m+1 m+2 2 2 dxm

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Q: 14. Let f(n) = n² + 20 and g(n) = n³. Show that f(n) is O(g(n)) by finding a positive integer N for…

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

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Q: Prove that (b − proja (b)) · a = 0.

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Q: Prove that x" dx „n+1 + C, n + 1 for n + -1.

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