Math 006 - Handout for Week 10

(1) Go over sample quiz
(2) Quiz
Short break - get your homework back etc
(3) A bit more on trigonometric functions
(4) Inverses of functions (page 299)
(5) Exponential and logarithmic functions (8.1): loga(c) = b means ab = c
(6) Start on derivatives of exponential functions (8.2)
Break, then Examples, tutorial
Note, assignment from week 9 is due in on Wednesday April 1, not March 25 as stated on handout for week 9.
Homework (not to be handed in) Assignment Due date: Wednesday April 8.
  • Please read pages 350 - 152 of text book
  • Ex 2 Page 352, Ex 1.(b) Ex 2.(b) Ex 3.(b) Ex 4.(b)
  • Ex 3 Page 354, Ex 1.(b) Ex 2.(b) Ex 3.(b)
  • Ex 8.1 Page 361, Ex 2.
  • Ex 8.2 Page 366, A. 1(a)-(e), Ex 4.(a)-(d)
  • (1) For f(x) = x + 3sin(x), what are the absolute maximum maximum and minimum on [0,pi]?
  • (2) Find x in each of the following:
    • (i) x = log3(1/3)
    • (ii) log2(x) = 5
    • (iii) 3 = 10x
    • (iv) logx125 = 3
  • (3) Using graph paper, sketch the graphs of (a) y = 6x (b) y = (1/4)x on the interval [-1,2]. Make a table with at least 5 values of each function, and clearly and neatly plot and label these points.
  • (4) Differentiate the following function:
  • x(ex + 1)
  • e(x2 + 3x +1)
  • e(x - 1/x)
  • (xe(x+1) - 1)e2x

Sample Quiz
There will be a quiz next week, which will be similar to the following question:
Find the critical values of the function

f(x) = e(x2 - 1) - 4x2

What you are expected to know about trigonometric functions
  • (1) d/dx(sin(x)) = cos(x)
  • (2) d/dx(cos(x)) = -sin(x)
  • (3) derivatives of functions involving sine and cosine, eg, x2cos(3x+1)
  • (4) Equation of tangent at a point for a function involving sine and cosine.
  • (5) If sin-1(a) = b is one value of sin-1(a), what are the others in [0,pi]?
  • (6) Using (5) to find the max and min of simple functions involving sine and cosine (you won't need to learn double angle formulars).

See previous weeks handout for tutorial times etc.