QUESTION 1
1.1 Integrate the following in terms of x:
$\int \left(\frac{1}{\sqrt{2x}} + 2^{-10x} + \frac{e^{-kx}}{2} - 4x^2 + 2\pi \cos wx - 5 \cos ec^2 5x\right) dx$
1.2 Evaluate:
$\int_0^{\frac{\pi}{4}} \sin 2x dx$
1.3 1.3.1 Draw the graph of $y = 2^x$, the X-axis, $x = 1$ and $x = 4$ and clearly indicate
the enclosed area. Also show the representative strip that will be used to
calculate the enclosed area.
1.3.2 Determine, using integration, the value of the enclosed area.
1.4 Simplify:
$\int (4e^x - 11x^3) dx$
QUESTION 2
2.1 Expand $\frac{1}{\sqrt{16x^2 + 4}}$ to four terms only by the use of the binomial theorem.
2.2 Differentiate the following in terms of x:
$y = \frac{5 + 6\sin x + x \cos x}{- \cos x} + e^{-6} - 2 \log_e x$
2.3 Determine, with the aid of differentiation, the coordinates of the maximum and
minimum turning points of $y = x^2 - 2x - 4$. Also distinguish between the maximum
and the minimum turning points by use of the second derivative.
2.4 Differentiate the following by using the quotient rule:
$y = \frac{\ln x^3}{\ln x}$
