ASSIGNMENT 1·12
There are two parts to this assignment. The first part is on WeBWorK — the link is available on the course
webpage. The second part consists of the questions on this page. You are expected to provide full solutions
with complete arguments and justifications. You will be graded on the correctness, clarity and elegance of
your solutions. Your answers must be typeset or very neatly written. They must be stapled, with your name
and student number at the top of each page.
1. Find the equation of the line tangent to the curve y = x sin4 (2x) at x =
2. Let


π
.
4
sin x
cos x
if x < 0
g(x)
if 0 ≤ x ≤ π .

cos(sin x) if x > π
Find g(x) such that f (x) is differentiable on the interval − π4 , ∞ . You must justify your answer.
f (x) =
3. Rockets are launched vertically from one of three pads at Cape Canaveral. In the initial part of its flight,
a rocket’s altitude is given by
t2
a(t) =
,
300
where a(t) denotes its altitude in kilometres t seconds after launch. The launch is supervised from the
Launch Control Centre (LCC), 5 kilometres away from the launch pad.
Imagine a camera at the LCC is pointed directly at the rocket throughout its launch. The camera swivels
as the rocket rises. Determine the rate, in radians/second, at which the camera is swivelling 30 seconds
after liftoff. (You will need a calculator; give your answer up to four decimal places.)