Methods2026 NHT Exam 1 · Q5Tech-free4 marks

Tangent function: asymptotes, derivative and area

Consider the function with the rule $f(x) = \tan(2x) + 2$ and maximal domain.

Find the equations of the vertical asymptotes for the graph of $y = f(x)$ .

1 mark

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Determine $f'(x)$ .

1 mark

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Find the area of the region bounded by the curve $y = f'(x)$ , the line $x = \frac{\pi}{12}$ , the line $x = \frac{\pi}{6}$ and the $x$ -axis.

2 marks

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