Linearizations

[InterserveVB]

Any ideas on how to do this?

Consider the following four functions:
f(x) = -1 + (2x+1)^1/2
g(x) = x^3 + x
h(x) = tan^2 x + x
j(x) = sin x

Find the linearizations of f, g, h, and j at a = 0.

Compute the values of each of these functions at x = .1 and the values of their linearizations

 

[tkhunny]

Is "linearization" in common usage? Does this mean the tangent line as some point? What does a = 0 mean for functions defined in terms of 'x'?

Read your definitions. Linearization of a function is defined as:

L(x) = f(a) + f'(x)*(x-a)

The last one looks easy enough,
j(x) = sin(x) -- j(a) = sin(a) -- j(0) = sin(0) = 0
j'(x) = cos(x) -- j'(a) = cos(a) -- j'(0) = cos(0) = 1

L_j(x) = 0 + 1*(x-a) = x-a

You do the rest and show your work.