81 The range of the function \( f(x)=2-x^{2}, x \neq 0 \) is \( \ldots \ldots \ldots \ldots \ldots \) \( \begin{array}{llll}\text { (a) }]-\infty, 2] & \text { (b) }] 2, \infty[ & \text { (c) }] 0,2] & \text { (d) }[0,2]\end{array} \)

Graph, state domain and range: \[ y=-3 \sqrt{x+3}+5 \]

j) \( \sin ^{-1}(y)+x^{3}=\sqrt{y} \)

(b) Find the angle between \( \overline{\mathbf{a}} \) and \( \overline{\mathbf{b}} \) where \( -6 \bar{a}+2 \bar{b}=2 i+j-8 k \) and \( 2 \bar{a}-\bar{b}=3 i-4 j+k \) (c) show that the line \( \frac{x-1}{2}=\frac{y-2}{-6}=\frac{z-1}{7} \quad \) is parallel to the tangent vector of the

1. Expand \( (1+x)^{\frac{1}{3}} \) in ascending powers of x up to the term \( x^{3} \). By substituting 0.08 for \( x \) in your result. Obtain an approximation value of the cube root of 5 .

12. The value of \( t \) is given by \( t=2 \pi \sqrt{\left(\frac{2.31^{2}+0.9^{2}}{2.31 \times 9.81}\right)} \) Without using a calculator, and using suitable approximate values for the numbers in the formula, find an estimate for the value of \( t \). (To earn th marks in this question you must show the various stages of your working.)