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Paper 2 – More about Areas
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Example
Let f ( x)
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� x . The following diagram shows part of the graph of f .
The point P ( a, f ( a )) , where a � 0 , lies on the graph of f . The normal at P crosses the
x -axis at the point Q ( b , 0 ) .
It is given that the gradient of [ PQ ] is
( a ) ( i ) Find f� ( a) .
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� . 3
( ii ) Hence , find a .
( iii ) Find b .
( iv ) Find the equation of [ PQ ] in the form y �mx � c .
( b ) Find the area between the graph of f , the normal at P and the x -axis .
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