P2.4 Binomial Expansion

Question 1

when is binomial expansion valid?

Answer 1

|x|<1
-1 < x < 1

Question 2

when are approximations based on binomial expansion more accurate?

Answer 2

when more terms of the expansion are used
when the values of x substituted into the expansion are closer to 0

Question 3

when is the expansion of (1+bx)^n valid?

Answer 3

when |bx| < 1
|x|< 1/|b|

Question 4

what is the method to expand (a+bx)^n?

Answer 4

a^n (1 + b/a x)^n

Question 5

when is the expansion of (a+bx)^n valid?

Answer 5

when |b/a x| < 1
|x|<|a/b|

Question 6

what is the method for binomial expansion with partial fractions?

Answer 6

1. split into partial fractions
2. work out each expansion separately
3. add or subtract the 2 expansions

Question 7

what is the method for using a substitution of x to find an approximation for a given value?

Answer 7

1. substitute in value for x into the expanded & non-expanded form
2. make the non-expanded form into the given value, doing the same to the expanded side