Chapter 1 And 2

Question 1

Difference of cubes (a^2 - b^3)

Answer 1

(a-b) (a^2 + ab +b^2)

Question 2

Perpendicular slope

Answer 2

Negative reciprocal i.e.) a/d becomes -b/a

Question 3

First principals method equation

Answer 3

Lim. [f(x+h) - f(x)]
h->0 ——————
h

Question 4

Instantaneous velocity equation

Answer 4

Same as first principals:
V(t) =lim. [f(t+h) - f(t)]
h->0 ——————
h

Question 5

Average velocity equation

Answer 5

=lim. [f(t2) - f(t1)]
t2->t1. ——————
t2-t1

Question 6

Rule #1 of infinite sequences

Answer 6

Lim. [1/n]. =0

N->infinity

Question 7

Rule #2 of infinite sequences (the forgotten rule)

Answer 7

Lim as n approaches infinity (r^n) =0 if |r| is smaller than 1

Question 8

Equation for infinite series

Answer 8

Sn=a(r^n-1)
       ———
        r-1
Where 
A= first term
R= common ratio
N= number of terms
Sn= sum of 'N' terms

Question 9

UDATED FORMULA FOR INFINITE SERIES THAT WE USE

Answer 9

Sinfinity = a/(1-r)
Where a= first term
r= common ratio

Question 10

Infinite series:
If |r| is smaller than 1:
If |r| is bigger than 1:

Answer 10

Smaller: will have a sum (convergent)
Bigger: won’t have have sum (divergent)

Question 11

Sum of cubes (a^3 + b^3)

Answer 11

(a+b) (a^2 -ab+b^2)

Question 12

Sketching a derivative graph

Answer 12

• max and min points become the x intercepts on the f’(x) graph
• determine whether the curves will have a positive or negative slope (going down towards point = negative therefore underneath the x axis and vice versa)

Question 13

Implicit differentiation

Answer 13

When taking the derivative of y always multiply it by (dy/dx)