| Date | None Specimen | Marks available | 6 | Reference code | SPNone.1.hl.TZ0.1 |
| Level | HL only | Paper | 1 | Time zone | TZ0 |
| Command term | Determine | Question number | 1 | Adapted from | N/A |
Question
QUESTION 1
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QUESTION 1
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Using l’Hôpital’s Rule, determine the value of\[\mathop {\lim }\limits_{x \to 0} \frac{{\tan x - x}}{{1 - \cos x}} .\]
[6]
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Markscheme
MARKSCHEME 1
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MARKSCHEME 1
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\(\mathop {\lim }\limits_{x \to 0} \frac{{\tan x - x}}{{1 - \cos x}} = \mathop {\lim }\limits_{x \to 0} \frac{{{{\sec }^2}x - 1}}{{\sin x}}\) M1A1A1
this still gives \(\frac{0}{0}\)
EITHER
repeat the process M1
\( = \mathop {\lim }\limits_{x \to 0} \frac{{2{{\sec }^2}x\tan x}}{{\cos x}}\) A1
\( = 0\) A1
OR
\( = \mathop {\lim }\limits_{x \to 0} \frac{{{{\tan }^2}x}}{{\sin x}}\) M1
\( = \mathop {\lim }\limits_{x \to 0} \frac{{\sin x}}{{{{\cos }^2}x}}\) A1
\( = 0\) A1
[6 marks]
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Examiners report
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