maths&statistics

1. solve the following equations for x
3(4^2(x+1))=2-29(4^x)
48(4^2x)=2-29(4^x)
48(4^2x)+29(4^x)-2=0
(3y+2)(16y-1)=0 y=4^x
y=-2/3 (rejected) or 1/16
So x=-2

2a. expand e^x^2 in ascending powers of x as far as the term in x^3
2b. hence, or otherwise, find the expansion of e^x+x^2 in ascending powers of x as far as the term in x^3.
(a)
e^(x^2)=1+x^2+x^4/2!+....
(b)
e^(x+x^2)
=(e^x)(e^x^2)
=(1+x+x^2/2+x^3/6+...)(1+x^2+x^4/2!+....)
=1+x+(1+1+1/2)x^2+(1+1/6)x^3+...
=1+x+(5/2)x^2+(7/6)x^3+...

第三條有沒有打錯﹐有開方號?

第三條, taylor expansion, differentiate 幾次再代0入去