Question

The linearization at a=0 to sqrt(1+2x) is A+Bx where A is____ and where B is _____?


A=?
B=?

Ty

Answer 1

the linearization is just finding a straight line that is close to the curve at the given point. That is just the tangent line. So, since when

y = √(1+2x),
y' = 1/√(1+2x)

y(0) = 1
y'(0) = 1
and the point-slope form for the line is

y-1 = 1(x-0)
y = x+1

A=1 and B=1

Check the graphs at

http://www.wolframalpha.com/input/?i=plot+y+%3D+%E2%88%9A%281%2B2x%29+and+y%3Dx%2B1+for+-.1+%3C+x+%3C+.1

You can see that at (0,1) the line and the curve are very close.