Newton's method is used to estimate the
- Verify that
and . (1 mark)
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- Using an initial estimate of
, find the value of . (2 marks)
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Calculus, MET2 2023 VCE SM-Bank 1
The function
- 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)
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- i. Find the equation of the tangent to the graph of
at the point where . (1 mark)
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- ii. Sketch the graph of the tangent to the graph of
at on the axes in part a. (1 mark)
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Newton's method is used to find an approximate
- Find the value of
. (1 mark)
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- Find the horizontal distance between
and the closest -intercept of , correct to four decimal places. (1 mark)
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- 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)
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- 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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Calculus, MET2 2023 VCE SM-Bank 7 MC
One way of implementing Newton's method using pseudocode, with a tolerance level of 0.001 , is shown below.
The pseudocode is incomplete, with two missing lines indicated by an empty box.
Which one of the following options would be most appropriate to fill the empty box?
