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Methods2023 Exam 2 Section A · Q9CAS active1 mark

Continuous and smooth piecewise function

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The function $f$ is given by

$f(x)=\begin{cases}\tan\left(\dfrac{x}{2}\right) & 4 \le x < 2\pi \\ \sin(ax) & 2\pi \le x \le 8\end{cases}$

The value of $a$ for which $f$ is continuous and smooth at $x = 2\pi$ is

1 mark

A

-2

B

-\frac{1}{2}

C

\frac{1}{2}

D

\frac{1}{2}

E

2

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tan(2x)sin(ax)

4≤x<2π2π≤x≤8

The value of $a$ for which $f$ is continuous and smooth at $x = 2\pi$ is