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Duration 2 Hours Part 1: MULTIPLE CHOICE QUESTIONS You may solve all questions. Each question is worth 2 marks. Your grade in this part is that of...

Find
dx
dy
if:
i.  
4
2 2 2

  
x
x x y x x e .
ii.
   
16
3 1 1
2
0 7 5

 

x
x x
y
.
.
b) Solve for x: .
x
e
14
2
1

Duration 2 Hours Part 1: MULTIPLE CHOICE QUESTIONS You may solve all questions. Each question is worth 2 marks. Your grade in this part is that of the best 5 questions, giving a total of 10 possible marks. Q–1: The domain of the function   x x x f 3 1 is a) R \{0} b) R \{0, −1} c) (0, ∞) d) (− ∞, 0) e) None of the above Q–2: The solution of the differential equation       10 0 2 P , x P x P is a)   x e x P 10 2 b)   x e x P 10 2 c)   x e x P 2 10 d)   x e x P 2 10 e) None of the above Q–3: The largest open interval(s) over which   x x x x f 12 3 2 2 3 is increasing is a) (−1, 2) b) (−∞,−1) c) (2, ∞) d) (–∞, −1) and (2, ∞) e) None of the above Q–4: The average value of the function   1 3 x x f over the closed interval [0, 8] is a) 31/9 b) 31/3 c) 248/9 d) 248/3 e) None of the above
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Q–5: The area of the region under the graph of f ( x ) = 3 x 2 + 4 and above x - axis on [0, 2] is a) 16 b) 8 c) 4 d) 3 e) None of the above Q–6: If     , x ln x f 2 then   e f a) ln (2 e ) b) 2 e c) e -2 d) e -2 e) None of the above Part 2: ESSAY QUESTIONS Each question is worth 10 marks. You should answer only FOUR out of the five questions, giving a total of 40 possible marks. Q–1: [6+4 Marks] a) Find an equation of the tangent line to the graph of   7 3 40 x x f at the point whose x -coordinate is 3. b) Find the points on the graph of   20 4 3 4 x x x f at which the tangent line is horizontal. Q–2: [5+5 Marks] a) Find the local maximum and minimum of the function   20 12 3 2 2 3 x x x x f . b) Determine the slope of the graph at the given point   1 3 2 4 2 3 , P , xy x y .
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