1. f0 02. 2. f 3. S 04 da z+e da z+e da x-e-8z 1 is divergent because ≤ and food is divergent x+ez 1 is convergent because ≤and is convergent x+e8z is divergent because and dis divergent x-e dx is convergent because ≤ and is convergent z+e&z 1 x+ez

Q: Find the value of the constant c that makes the following function co f(x) = = uous [cx + 7 cx² 7 if…

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Q: (lx) +3, x≤-3 Q4) Check the continuity of f(x) = -2x -3<x<3 " (6x + 2, x ≥ 3

A: To check the continuity of given function,

Q: (2x)" A) diverges if |2z| >1 B) diverges if |z| > 1/2

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Q: Show that an = 1/2n + 1 is decreasing.

A: Given: an=12n+1 Substitute 1 for n in the equation an=12n+1. a1=12(1)+1=13=0.333

Q: Q1- Choose or branch ( A-find the optimum values of X₁, X2, and X3 3X1 +2X2-X₁ = 1 2X1-2X2-4X3=2…

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Q: Determine if the function f(z) = is continuous. z²-1 Z-1 , z # 1 3, z = 1

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Q: Which of the following statements is not true for f(x)? S2+3 x 0 f(x) = o f(1) = 4 o f(0) = 3 %3D…

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Q: 2x+11 1 Consider f dx = x2+x-6 x-2 x+3 then evaluate S(-dx xp(* - 3 x+3

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Q: If (2 e)(1-3e-38) f(t) = C-¹ · L-₁ { (2²-0") (1 3e-1)} is continuous for t≥ 0, find f(1), f(2), and…

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Q: x < 2 2 < x < 5 at x = 2 and 5. x 2 5 4х, 2. Classify the discontinuity of f (x) = } x + 6, x² – 1,…

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Q: Q1) Check the continuity of the given function at the given c (or c's). 2-4z+3 if I+ 3 { (a) f(x) =…

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Q: Find the values of constants a and b that make f continuous on (-o0, +o0) where 2x +1 if a 5 f(x) =…

A: Use definition of continuous function and find the value of a and b

Q: Find a and b so that f(x) is continuous if f (x) = Ⓒa = ²/1 b = 60 96 a = - ²/2 b = 29/4/20 -²/26 =…

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Q: d(x) = [-x-k, if x = -1 2x+ 2k, if x = -1 k = 1 نی =-4 k=-1 k = 0 Determine k so that (x) is…

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Q: Q.4 A/ Prove the function continuous at x = -2, (x2 + 5 13-3x where %3D if x<-2 if x 2-2 f(x) = %3D

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Q: lex. min. {g, (x), g₂ (x)} 9₁ (x): -2x1 - x₂ ≥ 9 92 (x): X₁ X1 - 2x₂ ≥ 10 st. 2x1 + 5x2 ≤ 16 6x₁ +…

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