October 18, 2005
Lecturer: Dr Martin Kurth
Michaelmas Term 2005
Course 1E1 2005-2006 (JF Engineers & JF MSISS & JF MEMS)
Problem Sheet 2
Due: in the Tutorial 28 October / Lecture 01 November
Do not worry about your problems with Mathematics. I assure you mine are far
greater.
Albert Einstein (1879-1955)
1. Calculate the following exponentials, and express the result as Aeax .
(a) 10x ,
(b) 102x ,
(c) 102+x ,
(d) 4x b2x with b ∈ (0, ∞),
(e) 108x log 5 .
(5 points)
2. Invert the following functions. If necessary, restrict their domains to do
this.
(a) y = e2x ,
(b) y = 2ex ,
(c) y = ln(2x),
(d) y = log(2x),
(e) y = cos(2x).
(5 points)
3. Calculate
sin2 (θ) + cos2 (θ)
for all θ ∈ (−∞, ∞).
(*)
Questions 1 and 2 should be answered by all students, you will get points for them. Question 3
is more challenging and meant as an exercise for the more mathematically interested students.