(1) f(x) is (g(x)). Disprove the following statement. I It is always true that t(f(x)) is t(f(x)) is (t(g(x)))

Q: 1. 2. n−1 4 nh+n-6 7n+1 n² +1

A: We shall divide and using the highest power of n and then find the limit

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A: Determine the completely factored form of f(x) = x^(3) + 5 x^(2) - x -5

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Q: 5" n→∞ 72n+1 lim,

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Q: (b) Prove that Z/4Z is not a field.

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A: We have to determine the number of possible permutations of 7 things taken  at a time.So,

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Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. 4 4 ✓1.S=…

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Q: Let fn(x) = x^n for x ∈ [0,1]. check if it is pointwise convergence. Define where it becomes…

A: Given, fn(x) = xn , x ∈ [0,1].We will check poitwise convergence of fn on [0,1].

Q: Use the PMI to prove that 3-1 is even for all n E N.

A: To Show:  is even using the principles of mathematical induction

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Q: (7) Let m≥ 1 and let R= {0, 1, 2,...,m - 1}. (b) Prove that for every integer a there is a unique…

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Q: Prove that 1^2 - 2^2 + 3^2 +...+(-1)^(n+1)n^2 = (-1)^(n+1)n(n+1)/2 for all n∊N.

A: We will prove the given result by principle of mathematical induction.

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Q: Exercise 6.1.14: Find the Laplace transform of sin(w(t – a)).

A: We have to find the Laplace transformation of the given function

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Q: Use the binomial expansion to find the order of the following ex- pressions as x → 0. x3/2

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Q: In(x) - 6x² In(x) = -5 ln(x)

A: Given that the equation is:

Q: Source Demand 1 2 3 4 1 108 M M M 10 2 1.09 1.11 M M 19 Destination 3 1.11 1.13 1.1 M 29 4 1.13 114…

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Q: Solve the heat equation k a²u 0x² u(x, t) = = u(0, t) = 0, u(L, t) = 0, 0 0 (see (1) in Section…

A: Let u(x,t)=X(x)T(t)From the conditions:u(0,t)=X(0)T(t)=0u(L,t)=X(L)T(t)=0⇒ X(0)=X(L)=0From the…

Q: a. Given that v1 = eigenvalues. A₁ = X2 = [] and 72 = 4 are eigenvectors of the matrix -17 12 -18]…

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Q: Exercise 11. Recall the following Example of a topological space with the real line as underlying…

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Q: 12. Let xo < x < < x, and let f be continuously differentiable. Show that a f[xo, x₁, x₂] = f[xo,…

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Q: B.C. IC. Solve completely to the final form of the solution as a Fourier Series the heat equation…

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Q: 2. Consider matrices of the form 1 • (-² -²²2 ) + ² ( ¹4 ) B -2 (a) Mas 20. (b) Mas 20. Ma,a := a…

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Q: (a)Suppose that f is an injection. Show that f -1∘f(x) = x for all x∊D(f) and that f∘f -1(y)=y for…

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Q: d the orthogonal projection ŷ of y = 5 0 -5 = = Span u₁ = {-----})}) 4 , = 2 -4 onto the 3

A: The orthogonal projection of y onto span u1,u2 is

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Q: The function ƒ is defined by ƒ (x) = x³ – 5 sin (2x). Find all values of a that satisfy the…

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Q: of the A. Write te vertex Form of following quadartic Function +2+8x-20 y = 2²² +4 + + 2 1-y= 2.

A: For given 2 quadratic equation we have to find the vertex form of the equation .

Q: Suppose S represents any group that has the order |S| = R = 1,234,567, and suppose there is an n…

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