06 Promo _Question_19 Sep

# 06 Promo - 2 1 Find(a(b 2 dy for each of the following simplifying your answers in each case dx x y = ln x > 0 x 2[2[2 x = cos 2t y = t 2 The

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H2 MA 9740/S/2006 RJC JC1 Promotion Exam [Turn Over 2 1 Find d d y x for each of the following, simplifying your answers in each case. (a) ln 2 x y x = + , 0 x > . [2] (b) 2 cos 2 , . x t y t = = [2] 2 The diagram below shows the graph of ( ) f y x = . The points A , B and C have coordinates 1 ( ,0) 2 - , (1, 2) and (3, 1) respectively. Sketch on separate diagrams, the graphs of (i) f 2 x y = , [1] (ii) f 1 2 x y = - , [2] (iii) ( ) f ' y x = , where ( ) d f f ( ) d ' x x x = . [2] State, in each case, the coordinates of the points corresponding to A , B and C , where appropriate. 3 A curve C is given by the equation 2 ( ) 2 4 y x x - = + . (i) Find d d y x , giving your answer in terms of x and y . [2] (ii) Find the equation of the normal to the curve 2 ( ) 2 4 y x x - = + at the point (6,2) . [3] 4 A spherical ice ball melts at a constant rate of 3 1 10cm min - . When the radius of the ball is 6cm , find (i) the rate at which the radius of the ice ball is decreasing, [3] (ii) the rate at which the surface area of the ice ball is decreasing. [2] [The formulae for the volume and surface area of a sphere of radius r are 3 4 3 V r π = and 2 4 A r = .] x y ( ) f y x = C (3,1) B (1,2) 1 2 ( ,0) A - 0

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H2 MA 9740/S/2006 RJC JC1 Promotion Exam [Turn Over 3 5 A sphere of radius 1 m is inscribed in a right circular cone of base radius r and height
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## This note was uploaded on 10/12/2010 for the course C 11 taught by Professor Na during the Spring '10 term at Rappahannock Community College.

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06 Promo - 2 1 Find(a(b 2 dy for each of the following simplifying your answers in each case dx x y = ln x > 0 x 2[2[2 x = cos 2t y = t 2 The

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