Find the tangent line approximation for v(1+x) near x=0.

Question

Find the tangent line approximation for √(1+x) near x=0.

 

 

Answer 1

When x = 0, y = 1 for y = √(1 + x).

 

 

y'= 1/[2√(1 + x)]

 

The slope is y' evaluated at x = 0: m = ½.

 

 

The equation of the line has a slope of ½ and goes through (0,1).

 

y - 1 = ½(x - 0)

 

y = ½x + 1