Question

Which of the following is the linear approximation formula, L(x), that estimates values of y = ln(x) + 1 for values of x near 1?
a) y = x - 1
b)y = x
c)y = x + 1
d)y = -x

Answer 1

y(1) = ln(1)+1 = 0+1 = 1
y'(x) = 1/x
so, y'(1) = 1

You want the line through (1,1) with slope 1.