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18 Area

# 18 Area - 18 AREA 1 =x2(1x.=0and x=1. 2 =3 2xx2andy=5_

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y x 18. AREA 1. The diagram shows the graph of  y 2  =  x 2  (1 –  x ).  The curve cuts the  x -axis at  x  = 0 and  x  = 1.  Find the area of the loop. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ 2. Find the area of the region bounded by the curves  y  = 3 + 2 x  –  x 2  and  y  = -5. ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ ________________________________________________ VET Calculus 115 18. Area

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3. Suppose that  f(x)  =  . , sin 2 cos 3 π π - + x x x (a) [2 marks] Determine exactly the two zeroes  r 1  and  r 2  of  f . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (b)[5 marks] Calculate the exact coordinates of the maximum stationary point. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [3 marks] Determine the area of the region above the  x -axis bounded by the  x- axis and the graph of  f . __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 116 18. Area
VET Calculus 117 18. Area

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4. Consider the functions  f ( x ) =  2 1 ( x 2  – 5 x ) x  and  g ( x ) = -3 x . Points O (0,0), A and B are the points of intersection of the graphs of the functions  f  and  g . (a) Determine the coordinates of points A and B. [2] _________________________________________________________________________________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________________________________________________________________________________ _________________________________________________________________________________________________________________________________________________________________________________________________________________________
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18 Area - 18 AREA 1 =x2(1x.=0and x=1. 2 =3 2xx2andy=5_

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