Problem 5:

the approximate solutions is -0.281199574322961846512 after 7 iterations, and is correct to 21 digits

Problem 4:

1) x -x^3/6 + x^5/120 - x^7/5040 + O(x^8)

2)

1 - x^2/2 + x^4/24 - x^6/720 + x^8/40320 + O(x^10)

3) 1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+O(x^11)

A*B = [0 2] [1 3]

[1 4] [2 6]

= [ 4 12]

[ 9 27]

0 2 | 1 0

1 4 | 0 1

-2*row1+row2

0 2 | 1 0

1 0 | -2 1

1/2 row1

0 1 | 1/2 0

1 0 | -2 1

inverse is [ -2 1 ]

[ 1/2 0 ]

multiplies original by inverse

[ 0 2 | -2 1 ]

[ 1 4 | 1/2 0 ]

the product is the identity