Evalmote the Following lim i lim eイ×f5x 2) Um メ→3 [logs xア-1 3) lim log (3x²+2x)

Q: a) Describe the kernel and the image of Jn. (b) Use this to show that ??Jn is diagonalisable when n...

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Q: Consider the graph G given in figure below. Prove or disapprove that the graph is Euler? Hamilton? a...

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Q: 12. In an experiment, there are 5 bacteria in a petri dish initially. This bacteria doubles in every...

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Q: For this series of questions, we will evaluate a Taylor series approximation of the following functi...

A: The complete solutions are given below

Q: Solve the following systems of congruences. x = 4 (mod 7) 3x + 2 = 3 (mod 8) 2x = 5 (mod 3) 5x + 4 =...

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Q: 2. Prove that in any ordered field F, a? + 1 > 0 for all a e F. Conclude that any field with a solut...

A: Let F be any ordered field. We need to prove that, for any a ∈ F,   a2+1 > 0. We know that, in an...

Q: 6. A parallelogram is a quadrilateral with QUADRILATERALS that are parallelograms:(complete the word...

A: 6)A parallelogram is a quadrilateral in with  both pairs of opposite sides are parallel  

Q: Find the antiderivative of 25* dx. 25* + C In 5 A 5+2 + C 2 In 5 B 52r + C 2 In 5 25*

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Q: QUESTION 3 Suppose that you draw a point x in the middle of a page, and a curve going through X in s...

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Q: Find the inverse Laplace Transform of  F(s)= 6s/(s2+25) + 3/(s2+25). COMPLETE SOLUTION

A: The solution is given as  

Q: Bynsmg HAx)=l and H(x)=2v in Hernit polynomials, calculate the value of H()

A: In the given question, the concept of Hermit Polynomial is applied. Hermit Polynomial The Hermite Po...

Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x, ...

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Q: Solve the following integrals using any appropriate method of integrations: Jan a) xIn(3x +1)dx.

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Q: QUESTION 1 a) Given a function f(x)=x-3x-9x+2. i) Find the x-intercepts and y-intercept of f(x). ii)...

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Q: D Learning Task 1: Translate the verbal sentence to mathematical sentence. Use variable x to represe...

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Q: 2. Let u e R" and v e R" be two non-zero vectors, in other words at least one component of the vecto...

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Q: Is the equation y-4x²=36 represents y as a function of x?

A: yes the given equation represents y as a function of x given that y - 4x2=36 y = 36+4x2=4(x2+9)

Q: Simplify sinnh(loge(4)). Express ecos(3+iloge(4)  in the Cartesian form.

A: The given problem is to evaluate and simplify the given complex expressions and express in the Carte...

Q: Evaluate L{e* (cos at – sin nt s+3 A. (s+3)° – n² (s+3)² - – n² 2 S - 3 (s – 3)° – n² (s-3)° -R 2 2 ...

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Q: Show that 19nni se enoion gaiwollo tolo nsis oirlyan b-a b- |

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Q: Fourier Transform of

A: Fourier Transform:- It is a mathematical transform which decomposes functions depending on space or ...

Q: Assume that f : R → R is such that |f(x) – f(y)| 0 one has that f(r) – r f(0) + (1 – A)r (b) Consid...

A: Explanation Given - assume that f:ℝ→ℝ such that f(x)-f(y)≤λx-y for all x, y ∈ℝ and some λ∈(0, 1) To ...

Q: S5x sec?x dx 5.

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Q: .1.13 Do the odd permutations in S„ form a subgroup of S„? Why?

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Q: 7. The sine of an acute angle, 0, in standard position is What is the value of tan 0? a. 3 4 с. 4. 3...

A: We can solve this using formulas of Pythagoras and tan theta

Q: Let f(z)= for 0 <I<6, for 6 <z< 7. %3D Compute the Fourier cosine coefficients for f(z). Ao %3D %3D ...

A: Fourier cosine co efficient  A0=2L∫0Lf(x)dxAn=2L∫0Lf(x)cosnπxLdx  

Q: Find the cube roots of unity in rectangular form

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Q: form" of the Fundamental Theorem of Calculus: Let f : [xo, x1] → R be a continuous function. Then if...

A: NOTE:Kindly repost the other question as a separate question. 

Q: (5) Use the expansions (Maclaurin series) 1 (1) Ew", w| < 1 1- w n=0 1 (2) E(-1)"w", w|<1 1+ w n=0 t...

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Q: 4. Assume that a continuous function f : R –→ R is T-periodic; that is, f(x + T) = f(x) for all x E ...

A: given a continuous function f:ℝ→ℝ is T-periodic, defined as fx+T=fx ∀x∈ℝ to prove- for every natural...

Q: Kindly give proper explanation how you got the answer Boy has two bags of plums. Each bag has 10 plu...

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Q: Insert the indicated number of anithmetic means for cach of the following I. betwoen 6 and 16 (1 ari...

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Q: By using Ho(x)=1 and Hi (X)=2x in Hermit Polynomials, caleulate the Valne of Hg L)? (1)

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Q: Consider the basis B = } |0|, -- a. Find the coordinates of the vector i = | 1 rela b. Consider the ...

A: Introduction: A linear transformation matrix is one in which T(x)=Ax for a vector x in the domain of...

Q: 3. Let W be a subspace of R" of dimension k < n. Use the Fundamental Theorem of Linear Algebra to pr...

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Q: 2 Let a = -1 | and b = 1 | be two vectors 1 What is |al2|b|2 |a · b[? ?

A: Let us consider the vector v=x1,x2,....,xn then the magnitude of the vector is obtained as |v|=x12+x...

Q: 3d +4 What following laws of limits can i use for lim that equals or 1.75 d 14d2-2d+2

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Q: Find the Inverse Laplace of s+ 4 s2 +s - 6

A: Some of the properties of the Inverse Laplace function  L-1F(s)+G(s)=L-1F(s)+L-1G(s) L-11s-a=eat L-...

Q: . Irrational Prove using a proof by contradiction that the product of a nonzero rational number and ...

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Q: Evaluate Ln(-5.3-j2.4) O 4.3143 +j1.0541 O 1.7610 – j2.7164 O -1.2232+ j1.9883 O -2.6170 - j3.5246

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Q: Are the two graphs in the figure isomorphic? If there are isomorphic, label the vertices to show the...

A: The given graphs are: Now by labeling them, we have:

Q: label tiny 9 of 14 PROBLEM 4 Analyze each graph below to determine whether it has an Euler circuit a...

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Q: 2. Let u e Rm and v E R" be two non-zero vectors, in other words at least one component of the vecto...

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Q: 5. Assume that an ant moves on a plane continuously; that is, its coordinates x(t) and y(t) are cont...

A: (a) equation of unit circle can be written as - at (0.7,0.1) at (-2,3) we see the change in sign ...

Q: M9GE-IIle-1 Solves problems involving Parallelograms, Trapezoids and Kite. АСTIVITY 2: Read each ite...

A: according to our guidelines we can answer only three subparts, or first question and rest can be rep...

Q: x³ + 27 dx. x + 3 Find the antiderivative of 2x2 A + 9x + C 3 3x + 9 + C 2 B 3 3x2 9х + С + 3 2 - D ...

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Q: 1. Compute the first two steps of the Jacobi and the Gauss-Seidel Methods with starting vec [0,..., ...

A: system to solve using Jacobi and Gauss-Seidel Methods : 2u-v=0  -u+2v-w=2  -v+2w=0  

Q: There are 164 students in an Electronic Engineering (Computer) program where 110 students like Diffe...

A: The given situation can be represented by the following Venn diagram.

Q: Tessa has two pieces of cable, one 18 feet long and the other 10 feet long. For a science project, s...

A: Please find attachment for the details solution

Q: ne initial value problem d.x 3- teat ¤(0) : %3D %3D dt2 dt

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