11 Approximations

11 Approximations - 11. APPROXIMATIONS 1....

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11. APPROXIMATIONS 1. Let  f  be the function defined by  1 2 ) ( 3 2 - - = x x x x f (a) [1 mark] State the pole of the function. __________________________________________________________________________________ (b)[1 mark] Evaluate  ) ( lim x f x __________________________________________________________________________________ __________________________________________________________________________________ (c) [1 mark] Evaluate  ) ( lim x f x -∞ __________________________________________________________________________________ __________________________________________________________________________________ (d)[3 marks] State the  x  and  y  intercepts. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ VET Calculus 65 11. Approximations
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f(x) x (e) [6 marks] The derivative of  f  is given by  2 3 3 4 ) 1 ( 1 4 2 2 ) ( - + - + - = x x x x x f The numerator of  ) ( x f  has exactly two roots.  One of these roots is located at approximately 0.26, the  other root is near –1.  Use the Newton-Raphson method to refine the root near –1 to two decimal places. __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ (f) [5 marks] Classify each of the critical points of  f  as a local maximum, local minimum or point of 
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11 Approximations - 11. APPROXIMATIONS 1....

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