Evaluate the limit as x approaches 0 of ((2 + h)^3 -8)/h

[jan-willemreens]

...Good day Ms Shaw, During my search for YouTube channels about limits, I came across your channel, and I must admit that I was happy with what I saw. A kind of desktop with all the relevant algebraic formulas sheets at a glance, even the familiar triangle of Pascal is present; very convenient (lol). Studying the limit in your presentation makes me think of finding the derivative f'(2) of the function f(x) = x^3 at x = 2 applying " First Principles ", am I right? While you were evaluating the limit, I suddenly saw another way to evaluate the same limit, namely by considering the numerator as a difference of two cubes, according to your formula sheet: a^3 - b^3 = (a - b)(a^2 + ab + b^2), where a = (2 + h) and b = 2 --> we get the new expression for the numerator: (2 + h)^3 - 8 = ((2 + h) - 2)((2 + h)^2 + (2 + h)(2) + (2)^2) = (h)((2 + h)^2 + (2 + h)(2) + (2)^2), finally we can cancel the common factor h of numerator and denominator to obtain the evaluable limit: lim(h-->0)((2 + h)^2 + (2 + h)(2) + (2)^2) = 12 ... the f'(2), right Ms Shaw? It was a pleasure to watch your presentation... Thank you and take care, Jan-W