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Calculus, MET2 2023 VCE SM-Bank 1

The function is defined as follows.

  1. Sketch the graph of on the axes below. Label the vertical asymptote with its equation, and label any axial intercepts, stationary points and endpoints in coordinate form, correct to three decimal places.   (3 marks)

     

     

  2.  i. Find the equation of the tangent to the graph of at the point where .   (1 mark)

  3. ii. Sketch the graph of the tangent to the graph of at on the axes in part a.   (1 mark)

Newton's method is used to find an approximate -intercept of , with an initial estimate of .

  1. Find the value of .   (1 mark)

  2. Find the horizontal distance between and the closest -intercept of , correct to four decimal places.   (1 mark)

  3.  i. Find the value of , where , such that an initial estimate of    gives the same value of    as found in part . Give your answer correct to three decimal places.   (2 marks)

  4. ii. Using this value of , sketch the tangent to the graph of at the point where    on the axes in part a.   (1 mark)

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Show Worked Solution

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