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10 Curve Sketching

# 10 Curve Sketching - 10 CURVESKETCHING 1 f x =(a[2marks 4x...

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10. CURVE SKETCHING 1. Let  f  be the function defined by   ) 5 )( 2 ( 5 4 ) ( x x x x f - + + - = (a) [2 marks] State the poles of the function __________________________________________________________________________________ __________________________________________________________________________________ (b)[1 mark] Evaluate  ) ( lim x f x +∞ __________________________________________________________________________________ __________________________________________________________________________________ (c) [1 mark] Evaluate  ) ( lim x f x -∞ __________________________________________________________________________________ __________________________________________________________________________________ (d)[1 mark] Evaluate  ) ( 4 lim x f x __________________________________________________________________________________ VET Calculus 60 10. Curve Sketching

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f(x) x (e) [2 marks] State the  x  and  y  intercepts. __________________________________________________________________________________ __________________________________________________________________________________ (f) [7 marks] Show that there are no turning points and sketch the graph of  ) ( x f y = , clearly labelling  all the important features.  __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 61 10. Curve Sketching
VET Calculus 62 10. Curve Sketching

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2. If  6 10 3 ) ( 2 2 - + - + = x x x x x f , (a) [2 marks] State the domain of  f. __________________________________________________________________________________ __________________________________________________________________________________ (b)[2 marks] Evaluate  ) ( 2 lim x f x __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (c) [6 marks] Sketch the graph of  f  showing the intercepts, asymptotes and any other distinguishing features. _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ VET Calculus 63 10. Curve Sketching
f(x) x VET Calculus 64 10. Curve Sketching

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3. The graphs of a function  ) ( x f  and its derivative  ) ( x f  are shown below.
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10 Curve Sketching - 10 CURVESKETCHING 1 f x =(a[2marks 4x...

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