Evaluate the following limits. sinh r2 _ r2 1. lim r→0 sinhr −

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A: Solution :

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Q: Question 4 a) Soive DE 11 —y"+y² + y = o b) -15

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Q: 1: Add the following matrices. -1 2 13 -60 a) + b) 0 1 -2] 12 3 + 000 0 0

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Q: (b) Find the largest eigen value and the eigen vector for the matrix A = x¹ (0) = (1 1) 1² il where

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Q: II. Evaluate the following integrals 2x 2. S -dx 2 5+2x+x 2

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Q: .Given the following degree of the vertices of an undirected graph H = {4,1,5,3,4,3}, we can…

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Q: 6. List 5 similarities and 1 difference between the graphs of y = sinx and y = cosx. Similarities…

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Q: prove that for any fixed x > 0. Fix a constant r>1. Using the Mean Value Theorem era > 1+rx

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Q: Evaluate the following integrals 3 S- ª · |e* − e| + (e* + e) -dx e 0

A: It is known that: ∫eaxdx=1aeax+C. The absolute value function: y can be defined as: y=-y,y<0yy≥0.

Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

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A: Given as,  To find the problem which has shortest path.

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Q: Solve for x, sin²(x) + cos²(x)-1=0

A: Solution :

Q: 2. Which of the following operations is associative on Z? A. a*b = a b C. a*b = a B. a*b = max (a,…

A: Solution :  Options (c) is correct

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Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

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Q: Let R be the region below bounded by the graphs of C1: x2 + y2 = 16, C2: y = 4 − (x + 2)2, and C3: y…

A: Given,C1 : x2 +y2 =16 , C2 : 4-(x+2)2, and C3 : -4x-4

Q: 10. The inverse of the elements of A = {0,1,2} under a*b = (a+b) modulo 3 are A. 0' = 0, 1' = 1, 2'…

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Q: 4. Let f(x)=√√2 cosx - x (a) Determine the absolute extrema of the function f on the interval [플,플]

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: Evaluate J by means of trapezoidal rule using n = 10 and n = 20: 1 1 = [ exp(-x²)dx Note that this…

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Q: Suppose !=sinh2r, z= 6ư, 3s= cos2r are solutions of a linear homogeneous differential equation with…

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Q: 13. Which of the following is a subgroup of (R+, *) where a*b = (ab)/2? (Q, *) A. B. (Z, *) C. (Q+,…

A: Given that                    ℝ+, * is a group             where…

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Q: 4. Find the measure of the angle between u = 6i - 3j and v = 2i + j to the nearest tenth of a…

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Q: 4. Solve the trigonometric identity: sin4x = 2sin2xcos2x.

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Q: Question 4 Find the equation of the tangent line to the curve Y = (2-6³²) cos(₂x) at x=0

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Q: 4. Evaluate the double integral: L Lade 1/3 27 +1 (Hint: Change the order of integration to dy dx.)…

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Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

A: let A be a nonempty subset of a bounded set B. why does infA and supA exists? show that  (a)…

Q: 9)THE ELEPHANTS Recently, a study on the African and Asian elephant populations was published. The…

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Q: 13 2 1 Given A = 2 13 3, find wwww 4 2 1] the lower triangular matrix. [3 0 0 a. 2-1/3 0 C. [4 −2/3…

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Q: (a) Solve the differential equation ' + y + y = 0. (b) Use the method of undetermined coefficients…

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Q: Use variation of parameters to solve the differential equation x²y" + y = x. [Leave u₁ and u₂ in…

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Q: What is the volume in cubic units of the solid formed when the region bounded by x = y - y^2 and x =…

A: This is a problem of Volume of rotation.

Q: Put the following program in matrix standard form Minimize Z= 2X₁-2X₂+4X3 Subjected to:…

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Q: Use local linear approximation to estimate √(3.95)³

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Q: Use a backward difference to approximate the derivative of f (x) = cosh x at x = 2 using h = 0.01 O…

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