4" - 1 25. Find lim 1-0 3x - 1 (a) log; 4, (b) In(4) - In(3), (c) 1, (d) 3 ln(4) - 4 ln(3), (e) 4/3.

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8 Nov 2018

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4" - 1 25. Find lim 1-0 3x - 1 (a) log; 4, (b) In(4) - In(3), (c) 1, (d) 3 ln(4) - 4 ln(3), (e) 4/3.

Answered

8 Nov 2018

2. BRIEF SOLUTIONS (2 MARKS EACH Give the numeric value of each of the following limits if it exists; if the limit is too or -o, write too or-o respectively. In all other cases write "NO FINITE OR INFINITE LIMIT”. 1 1 (a) lim arctan (1- x 21+ ANSWER ONLY

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7 Nov 2018

1. Let A be an 8 x 5 matrix such that the system Ax = 0 has only the trivial solution x = 0. What is the dimension of the row space of A ? (A) O (B) 3 (C) 5 (D) 7 (E) 8

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6 Nov 2018

() afmetion to define sa tulons (9) A function is defined as follows f(x) = {|r - 31+ az 12 - ar +2 if I<2 if > 2. Find the value of a such that f(x) is continuous at I = a.

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6 Nov 2018

(6) Find the horizontal asymptotes of the curve y = x2 + x - x2 +1.

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5 Nov 2018

(b) Find an equation for the plane that contains L and is parallel to the line of intersection of 7 and '.

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5 Nov 2018

(10) A function is defined as follows SI - 2 + arif r <1 12? + 2ax - 3 if > 1. Find the value of a such that f(x) is continuous at r = a. Answer:

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3 Nov 2018

) / 2 1 (-1 of R3, the co-ordinate ) / 1 / 0 11. Given the orthogonal basis B = {1 -1 .11 1 1 (1) vector of v=(1,1,0) relative to this basis is A) (0,1,1) B) (0, -1,1) c) Gas-1, V6T D) (0,1,1)

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2 Nov 2018

8. (10pts) Consider the line L that passes through the points A(-1,0,0) and B(2,3,3), and the planes 7: -2.+ 2y + z = 5 and 7' : x +2= -1. (a) Find the intersection of L and .

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1 Nov 2018

(c) Find a diagonal matrix D and an invertible matrix P such that A= PDP-1 (do not compute P-1).

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31 Oct 2018

6. (10 marks) A farmer wants to fence a rectangular field of 5000 square meters, and then divide it into three equal parts by fences all parallel to one of the sides of the rectangle. What shape of field will minimize the cost of the fencing? Fully justify your answer!

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31 Oct 2018

8. Let f(x) = z^ \n(x2 + 7). Then f'(2) is (a) 32 ln(11) + 4/11, (b) 32 In(11) + 16/11, (c) 32 ln(11), (e) 32 ln(11) + 16. (d) 32 In(11) +64/11,

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30 Oct 2018

5. (15 marks) Let f(x) = (In x)2. (c) Find and classify all local extrema and determine the intervals of increase and decrease off.

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28 Oct 2018

1: 18. Find lim sin(2) (a) 1/2, (b) 1, (c)-1, (d) 0, (e) does not exist.

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28 Oct 2018

[3 MARKS EACH) Answer each question. (a) A ladder 30 feet long rests against a vertical wall. A 3-foot rope hangs down from the top of the ladder, with a lantern attached to it. If the bottom of the ladder is slipping away from the wall at a rate of 1 ft/s, how fast, in ft/s, is the lantern descending when the bottom of the ladder is 10 feet from the wall? ANSWER ONLY

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23 Oct 2018