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Unformatted text preview: for a function to be continuous at a point x = a . Answers: (a) The picture is the graph of y = x 3 with the part over [2 , 3] removed and replaced by a horizontal line at height 1 5 . (b) It is not continuous at x = 2 and at x = 3, (c) because the left and right limits are dierent at those two places. 4 In this question derivatives may be evaluated by any (correct) method. (a) If f ( x ) = x 2-9 x 2-7 x +12 , nd f ( x ) and f (2). (b) If y = (cos x )(2 + 3 x ), nd dy dx . (c) If g ( t ) = 2 t 1100 , nd g (1). (d) If h ( u ) = cos u u , nd h ( u ). Answers: (a) f ( x ) =-7 ( x-4) 2 ; f (2) =-7 4 (b) dy dx = (-sin x )(2 + 3 x ) + 3cos x (c) g ( t ) = 2200 t 1099 (d) h ( u ) = (-u sin u )-(cos u ) u 2 5 Find the equation of the line which is tangent to the curve y = x 1+ x 2 at the point (3 , 3 10 ). Answer: y =-2 25 x + 27 50...
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