x₁ + x₂ + +x. Prove that -x₁)(1+x₂)... (1+x) ≤1+S+ ... S² S³ + 2! 3! +...+ uS - n!

Q: Find the length s of the path (3 + 10r,9 + 2r312) over the interval 5 < t < 6.

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Q: Evaluate (Vx+ f. d dx. OA. A. Vx2 + 2 + a² - a In + C O B. Vx2 + a² - In |x| C. Vx2 • a? + In- + C…

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Q: 2. Solve: 3 -X-2 x²- 11 1 X x=²=₂+x²= 1² and state any NPV's. X-2 X+1

A: This is question of calculus.Here one equation is given We have to solve it.And state the…

Q: Evaluate: L(e* -3t * sinh 7t).

A: Given: Le-3tsinh7t

Q: Q:- Show thet B(n, n) B( n+on+=2 1-40

A: The solution is given as

Q: 4. Prove that x*+2x²+5 + x²+2x*+6 =0 x-1 x-7 has a solution between 1 and 7.

A: We need to solve the polynomial.

Q: 4 Lonsider the functlan fx)= -5x4- |l+x?tx-17. functfon Fex)= -5xH-|l+x²+2x-17. 5xH-113+ Whatis r n…

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Q: Show that m > (2). m! = (2″ − 1)(2″ − 2) (2¹ – 2²)... (2¹ — 2n-1). -

A: The given problem is to show the following condition m&gt; nC2 for the given inequality.

Q: . Show that p(X) = XP-1 +... +X +1 when p is prime.

A: For every integer n≥1, the nth cyclotomic polynomial Φn is the monic polynomial whose complex roots…

Q: b) Prove that |x| ≤ 1 implies that |x² + 2x - 3| ≤ 4|x − 1].

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Q: 5- Find L-1 5² (s²+4)² by using Convolution theorem.

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Q: (c) Prove that for n ≥ 1, n [27/7/2≤2- j² 1 n

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Q: Let A = {x € R : x < a} and B={x €R: x < b}, where a and b are real numbers. Show that sup(A+ B) =…

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Q: if |z² + 1| = 2| z+1|  z e C then | z|  <= sqrt*7 Prove.

A: Given  z2+1=2z+1 , z∈ℂ            (i) Now,   z2+1=2z+1z2+12=4z+12 ,…

Q: f6) = 5-31 5+3x Q11. Let %3D

A: Given: To Find:

Q: If I (F14)- s²+1 SO is given by? a) V(s? + 1)³

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Q: (a) [0, 1] (c) {2,7} (e) {÷ :n e N} (g) [0, 1] U [2, 3] (b) (0, 1) (d) {T,e} (f) {0}

A: To find supremum of given sets .

Q: show that |z3|  ≠ |z4|  it is verified that |z1+z2/z3+z4|  ≤ |z1|+|z2|/|z3|-|z4|

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Q: Show that (c + V² – x \c – V² - x. + V² – x²) – In = 2 In(c 2 In x

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Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

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Q: Determine inf H and sup H for H = (-1, 0), H = {0, 1}U(2, 3),

A: As per the guideline i am uploading the first two. For the other two kindly resubmit the questions…

Q: 9. Solve In (x+5) 2 2. O A. (x | x 2 12.3891} B. (x | x 2 2.3891} O C. (x |xs 12.3891} O D. {x |x s…

A: Given:         ln(x+5)≥2

Q: let fAg be funcbions that sabis fy fla)= -4 A g la)=-9. find h'la) for: a) h(x) = 2f(x) c) h(x)= 10…

A: Since multiple sub parts ate asked, I am answering first 3 subparts.

Q: Use proof by contradiction to show that no integers  y and z exist for which 24y + 12z = 1.

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Q: (3c) Let n E Z. Prove that if n is odd, then 4|(n² – 1)

A: here is the proof

Q: es (or+.1). COS Using P, (x), eshimate cas

A: In the question it is provided a function fi=cosπ+i The objective is to estimate the above function…

Q: 3. Show that all integers n ≥ 2 can be expressed as 2x + 3y for some nonnegative integers r and y.

A: Mathematical induction is a proof technique used in mathematics to establish the truth of a…

Q: Find the length of (3et − 3, 4et + 7) for 0 ≤ t ≤ 1

A: To find the length

Q: () - (" ;')-(,".) Show that: n+1

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Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

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Q: 1. Find L-'[l/(p² + a?)²] by convolution.

A: Let 1p2+a22=1p2+a2p2+a2=1p2+a2p2+a2= FpGp      Then ft=gt=sinata

Q: The value of x which satisfy 3x + 1| < - is : 5.

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Q: Find: ii) P (X₂ ≤ 1X₂ ≤). f(x₁,x₂) = {1x1x² 0≤x≤1, 0≤ x₂ ≤ 1 elsewhere

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Q: Let (t)= a. b. 2 53 (t² + 1 (t²-t 1|SL|SII e - e if 0 ≤ t < 2 if 2 st C ++ 211212 C. c. +-e-²5+/ d.…

A: