Evaluate the limits of the following functions as x → 0 sin² x x² f(x) = e (b) f(x) = x ln (x) (c) f(x) = 1-cosh (x) x²

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Q: Find the multiple solutions. Maximize z = 15x₁ + 10x₂, subject to 2x₁ + 9x₂ ≤ 144 3x₂ ≤ 60 Z = 2x₁ +…

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Q: Set up the simplex tableau. Do not solve Maximize z=135x1 + 255x2 85x1 + 64x2≤530 75x1 + 37x2≤130…

A: Given Linear programming problem is: Maximize z=135x1+255x2 85x1+64x2≤53075x1+37x2≤13024x1+12x2≤92…

Q: 00 Show that 8 Σ anx" n=3 n=4 Σ nbnx" n=4 How can the two series be combined into a single sum? _n-1…

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Q: Define T: R2 R² by T(x1, x2) = (x2 +3, x₁ + 4) (a) Find u € R² and L = O(R²) such that T = T₂ o L.…

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Q: Homework 3.10. For the first order differential equation y' = y/t+t cos(t), with initial condition…

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Q: (4). Suppose that f: G→ G' is a monomorphism, G is a non-trivial group and G' is non-abelian. Then G…

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Q: Let A = x-2 3 1 x-4 3 2 x-6x3 For which values of r a) the matrix has no inverse, b) its columns are…

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Q: (4) V2 = A basis for R³ consists of the three vector V₁ = , V3 = 1 2 3 " (You do not have to verify…

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Q: Compute oro-1, where o = (1, 2) (1, 3, 5), T= (1,5,7,9). List all the conjugate classes in S3.

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Q: Evaluate the complex integral rx+yi [*** az (ebz² +c) dz v if a = 5.7, b = 0.5, c = 3, v = 4, x = 1…

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z)=tan(4x+y+z). F(x, y, z) -

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Q: d'y dx² ==y+sinx, y(0)=1.0, y(2) = 3.0. 0≤x≤2,

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Q: Find the radius of convergence, R, of the series. R = V 8 I = n = 1 _(x + 4)" Find the interval, I,…

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Q: (c) Prove that HK/K is isomorphic to H/(H ^ K). (Hint. What is the kernel of the surjective…

A: Since you have asked multiple questions, we can solve one question for you. If you want other…

Q: Consider the following vectors in R³: 5 12 7 -7 11 Find a basis of Span (V₁, V2, V3, V4, V5). V1 =…

A: Given That :  Vectors in R5 are  v1=5127-7-11 , v2=102414-14-22 , v3=76-11-13 , v4=-3-30-1-5 ,…

Q: Prove that F(x, y, z) = (y² cos x+z³)i+(2y sin x-4)j+(3xz+2)k is a conservative vector field.

A: As per our guideline, we are supposed to solve only first subpart. Kindly repost other subpart as…

Q: The function f(x) = x³ - 6ax² + 5x satisfies the conditions of Lagrange's mean value theorem over…

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Q: The group SO(1,2) is defined as SO(1,2)= {A E GL3(R): ATnA = n}, where is the diagonal matrix η with…

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Q: The squence is 1 + 4 + 16 + 64+ ... + 4^n. I know the common ratio is 4, and to use ((r^n) -1)/(r-1)…

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Q: 12. Solve each of these congruences using the modular in- verses found in parts (b), (c), and (d) of…

A: (a) 34x ≡ 77 (mod 89) Here (34, 89) = 1 =&gt; 89 - 34 = 55 So 55 is the inverse of 34 in modular 89.…