Consider the family of functions
- Write down the equations of the two asymptotes of the graph of
when . (2 marks)
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- Sketch the graph of
for on the set of axes below. Clearly label any turning points with their coordinates and label any asymptotes with their equations. (3 marks)
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- i. Find, in terms of
, the equations of the asymptotes of the graph of . (1 mark)
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- ii. Find the distance between the two turning points of the graph of
in terms of . (2 marks)
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- Now consider the functions
and , where and . - The region bounded by the curves of
and is rotated about the -axis.
-
- Write down the definite integral that can be used to find the volume of the resulting solid. (2 marks)
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- Hence, find the volume of this solid. Give your answer correct to two decimal places. (1 mark)
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- Write down the definite integral that can be used to find the volume of the resulting solid. (2 marks)
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Show Worked Solution
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d.ii.
♦♦ Mean mark (d)(ii) 37%.
