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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

Evaluate \(\mathop {\lim }\limits_{x \to \infty } \dfrac{{\left( {2x – 1} \right)\left( {x – 2} \right)}}{{\left( {x – 1} \right)\left( {x + 2} \right)}}\).

CorrectIncorrect - Question 2 of 10
##### 2. Question

Use the first principles to find \(f’\left( 2 \right)\) for \(f\left( x \right) = \dfrac{1}{{2x – 1}}\), correcting to two decimal places.

CorrectIncorrect##### Hint

\(f’\left( a \right) = \mathop {\lim }\limits_{h \to 0} \dfrac{{f\left( {a + h} \right) – f\left( a \right)}}{h}\)

- Question 3 of 10
##### 3. Question

Find \(\dfrac{d}{{dx}}{\log _e}\left( {{x^2} – 1} \right)\left( {{x^2} + 2} \right)\).

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}{\log _e}f\left( x \right) = \dfrac{1}{{f\left( x \right)}} \times f’\left( x \right)\)

- Question 4 of 10
##### 4. Question

Find the point on the curve \(y = {x^2} – 5x + 4\) where the tangent is perpendicular to \(y = \dfrac{x}{5}\).

( , )

CorrectIncorrect - Question 5 of 10
##### 5. Question

Find the maximum and minimum values of \(P = 200 + 50\cos \dfrac{{\pi t}}{4}\).

maximum = , minimum =

CorrectIncorrect - Question 6 of 10
##### 6. Question

Given that \(\dfrac{{{d^2}y}}{{d{x^2}}} = 2x + 3\), \(\dfrac{{dy}}{{dx}} = 12\) when \(x = 2\), \(y= 5\) when \(x = 1\), and \(y = \dfrac{{{x^3}}}{p} + \dfrac{{3{x^2}}}{q} + rx + \dfrac{7}{s}\) find \(p\), \(q\), \(r\) and \(s\).

\(p = \) , \(q = \) , \(r = \) , \(s = \)

CorrectIncorrect - Question 7 of 10
##### 7. Question

Evaluate \(\int_{ – 1}^4 {\sqrt {3x + 4} } dx\).

CorrectIncorrect - Question 8 of 10
##### 8. Question

Find \(\int {{{\cos }^4}x{{\sin }^5}xdx} \).

CorrectIncorrect##### Hint

\(\dfrac{d}{{dx}}\cos x = – \sin x\)

- Question 9 of 10
##### 9. Question

Find \(p\) and \(q\), if \(\int {\dfrac{{3x}}{{\sqrt {{x^2} + 8} }}} dx = p\sqrt {{{\left( {{x^2} + 8} \right)}^q}} + C\).

\(p = \) , \(q = \)

CorrectIncorrect##### Hint

- Question 10 of 10
##### 10. Question

A particle has velocity function \(v\left( t \right) = \cos 3t\) cm/s as it moves in a straight line. The particle is initially 0.5 cm to the right of the origin. Write a formula for the displacement function.

cm

CorrectIncorrect