Use tangent line approximation to derive an estimate for (1+x)^n, when x is near 0, and n is any real number.

when x is zero, (1+x)^n = 1

derivative = slope = n ( 1+x)^(n-1)
when x is close to 0, = n
so through the point (0,1) and slope = n
y= n x + 1