Question

estimate change in f using the linear approximation and compute both error and the % error

f(x)= (3+x)^1/2

a=1

change in x=0.5

Answer 1

I tried to answer but Jiskha will not allow me to post my reply.
In general calculate f(1) = 2
f(1.5) = 2.1 something
that is exact to the accuracy of your calculator

then calculate f(x+dx) = f(x)+ dx (df/dx)
where df/dx = .5/(3+x)^.5
which is (.5 / 2).5 = .125
so f(1.5) = 2.125 linear approximation

error = 2.125 - exact
percent = 100 * error/2.1whatever)

Answer 2

Help someone, I can no longer reply to questions as me.

Answer 3

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