Question

Find linear approximation of √1+xaround x=0 involves estimating:

a) The tangent line at x=0.
b) The slope of the function at x=0.
c) The derivative at x=0.
d) The integral around x=0.

Answer 1

To find the linear approximation of √(1+x) around x=0, we can use the tangent line at x=0, which is y=1.

Step-by-step explanation:

To find the linear approximation of √(1+x) around x=0, we can use the tangent line at x=0. The tangent line at x=0 is the line that touches the curve at that point and has the same slope as the curve at that point.

In this case, the tangent line is just the line y = 1, since the slope of the function √(1+x) at x=0 is 1.