Mathematics

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What is the value of \({\sqrt[3]{24} \times 3^{^2/_3}}\)? [2 points]

1. \(6\)
2. \(7\)
3. \(8\)
4. \(9\)
5. \(10\)

For the function \(f(x)=2x^3 - 5x^2 + 3\), what is the value of \(\displaystyle\lim_{h\to 0} \dfrac{f(2+h) - f(2)}{h}\)? [2 points]

1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
5. \(5\)

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For \(\theta\) that satisfies \(\dfrac{3}{2}\pi < \theta < 2\pi\) and \(\sin(-\theta) = \dfrac{1}{3}\), what is the value of \(\tan\theta\)? [3 points]

1. \(-\dfrac{\sqrt{2}}{2}\)
2. \(-\dfrac{\sqrt{2}}{4}\)
3. \(-\dfrac{1}{4}\)
4. \(\dfrac{1}{4}\)
5. \(\dfrac{\sqrt{2}}{4}\)

If the function

\( f(x) =\begin{cases}3x-a & \; (x < 2)\\\\x^2+a & \; (x \geq 2)\end{cases}\)

is continuous on the set of all real numbers, what is the value of the constant \(a\)? [3 points]

1. \(1\)
2. \(2\)
3. \(3\)
4. \(4\)
5. \(5\)