QUESTION 1 [13 MARKS
(a) Fill in the blanks with appropriate answer
1
(i) The domain of the function $f(x,y) = \frac{1}{\sqrt{25-x-y}}$ is ______ and
the range is ______
(ii) In the equation $a = 3T + 2N$, the normal component of acceleration is equal to ______ and the tangential component of acceleration is equal to ______.
[4 Marks]
(b) Given the vector valued function $r(t) = 3\cos(2t)i + 3\sin(2t)j + 3tk$. Find the following:
(i) unit tangent vector $T(t)$,
(ii) principal unit normal $N(t)$,
(iii) curvature at $t = 0$.
[9 Marks]