Question

(a) Find the tangent line approximation for sqrt(9+x) near x=0.

(b)Find a formula for the error, E(x),in the tangent line approximation found in part (a).

For part A, is the answer y=3. For part b, I don't understand , any help would be greatly appreciated.

Answer 1

(a) What they are calling the "tangent line approximation" is usually called the first two terms of a Taylor series.
If f(x) = sqrt(9 + x), for small values of x, f(x) is very close to
f(0) + df/dx(0) *x
= 3 + (x/6)

(b) The difference between the actual value of sqrt(x+9) and the tangent line approximation is
E(x) = sqrt(x+9) -3 - x/6

Answer 2

find tangent line approximation of 2 over x+9