There are three parts to this assignment.
Part A is to be completed online before 7:00 a.m. on Friday,
January 14.
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 focuses on fundamental skills and computations. It can be found online, labelled
A1 , 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 Just-In-Time text, complete question 4 from appendix C.4. From the Calculus: Early Transcendentals text, complete question 54 from section 3.4.
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. Find the equation of the line tangent to the curve y = 2 x which passes through the point (1 , 0).
2. Solve the equation x x x
. .
.
= e for x . (The exponent tower is infinite.)
3. Note that
1
2
1 / 2
=
1
4
1 / 4
.
Prove that there are infinitely many distinct positive numbers a and b satisfying a a and then sketch, f ( x ) = x x .)
= b b . (Hint: minimize,