3. Consider the function f(x) = 12 - Vx| (c) [3 marks] Using your answer in part (b), show that f(x) is continuous on its domain. Justify your answer.

Answered

21 Dec 2017

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3. Consider the function f(x) = 12 - Vx| (c) [3 marks] Using your answer in part (b), show that f(x) is continuous on its domain. Justify your answer.

Answered

21 Dec 2017

9. (8pts) Consider the linear transformation T:R2 R3 defined by (x + 4y -C 3y and the linear transformation U: R3 ©)-(3) •©–0). ()-(6), «()-(-) R2 such that (a) Find the matrices of T and U.

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18 Dec 2017

7. Suppose that 4 and -2 are the only eigenvalues of the matrix A. Which of the following statements is true? (a) 41-A is invertible, and there is a nontrivial solution to Av = -2v. (b) det (41+ A) = det(21 - A) = 0. (c) 41 - A is not invertible, and there is a nontrivial solution to Av = -2v. (d) det(41+ A) = 0, and there is a nontrivial solution to (21 - A)v = 0. (e) none of the above

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15 Dec 2017

la a2 a3) 4. (pts) Let A= a2 a3 a a3 a a (a) Calculate det A.

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15 Dec 2017

17. Let f(x) = * - 9x2 - 273.x - 2. The function f has a point of inflection at x = (a) -1, (b), (c) 4, (d) 10, (e) 13.

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14 Dec 2017

(b) Where the system has infinitely many solutions, write these in parametric form.

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14 Dec 2017

1. (10 marks) Determine the following limits: (a) lim ( x2 - 4x +3 - x2 +1) tan-x (6) lim x=0 secx - 1

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13 Dec 2017

(5) Using the definition of the derivative show that the function so /-r2 - 22 f(x) = 1 +2 if r -1. is not differentiable at r = -1.

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12 Dec 2017

5. (15 marks) Let f(x) = (In x)2. (d) Find the absolute minimum and the absolute minimum value of f. Justify!

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11 Dec 2017

2.2 ( 10 points) Given the points A(1,1,1), B(2,3,5), C(4,2,3), D(3,4,2) (a) Show that A, B, C, D are not coplanar (ie do not lie in a common plane).

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11 Dec 2017

(3) Is there a number which is 2 less than its cube?

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10 Dec 2017

(d) Find a basis for the null space of M.

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10 Dec 2017

2. Suppose that C is a mxn matrix D is a pxq matrix, F is a r X s. Assume that the matrix CDT +CFT is well defined. Which of the following is true? (A)m=n=s=q and p=r B) m =n=p=q=r=s. C) m=n=p=s and q=r. D) m = p=n=. E) None of the above.

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9 Dec 2017