What is the slope of the line through (3,9) and (x,y) for y=x^2 and x=2.97? x=3.001? x=3+h? What happens to this last slope when h is very small (close to 0)?

Question

Help please!! not sure with my computation. Thank you.

Answer 1

Slope=(x^2-9)/(x-3) where x=2.97, 3.001 and 3+h.

(x^2-9)/(x-3)=(x-3)(x+3)/(x-3)=x+3.

x=2.97: (2.97^2-9)/(2.97-3)=2.97+3=5.97.

x=3.001: 6.001.

3+h: 6+h which becomes 6 as h approaches zero.