# ASSIGNMENT 8 for SECTION 001

```ASSIGNMENT 8 for SECTION 001
There are three parts to this assignment. Part A is to be completed online before 7:00 a.m. on Friday,
November 19. Part B and Part C, which require full solutions, are to be handed in at the beginning of class
on the same date.
Part A [10 marks]
This part of the assignment can be found online, labelled A8, at webwork.elearning.ubc.ca — sign in using
the MATH110 001 2010W button.
Part B [5 marks]
This part of the assignment is drawn directly from the course texts. It focuses on mathematical exposition;
you will be graded primarily on the clarity and elegance of your solutions.
From the Calculus: Early Transcendentals text, complete question 72 from section 3.3 and question 72 from
section 3.6.
Part C [15 marks]
This part of the assignment consists of more challenging questions. You are expected to provide full solutions
with complete arguments and justifications.
1. Let f1 , f2 , . . . , fn be n differentiable functions. Prove that
0
(f1 f2 &middot; &middot; &middot; fn ) = f10 f2 f3 &middot; &middot; &middot; fn + f1 f20 f3 &middot; &middot; &middot; fn + &middot; &middot; &middot; + f1 f2 &middot; &middot; &middot; fn0 .
2. Find the derivative of f (x) =
esin(cos x) +
2x
x−1
1000
.
3. A nuclear detonation at ground level emits a blast wave that expands radially, like a circular ripple, at
a speed of 30 km/second. Find the rate of expansion of the area contained within the blast wave 0.1
seconds after detonation.
```