Find the linearization of: y=sinhx at x=0

Please show all work so i can see how to do it
If you scratch my back il scratch ur back

http://en.wikipedia.org/wiki/Linearization

doesnt seem too hard

Is my work correct?

Find the linearization of: y=sinhx at x=0

linear approximation = f(a) + f'(a)(x-a)

d/dx sinhx = coshx

f(0) = 0

f'(0) = 1

By plugging those into the linear approx formula we get:
f(0) + f'(0)(x-0)
0 + 1(x-0)
1x
x <--------------------- answer is x

that looks right.

now try to think about this for a second.

draw the graph of sinh(x). And look at the slope of the line at the point x=0. Does it look like that line is y=x?

Here is the graph:



Looks like it to me!