Chapter P - P.3 - Functions and Their Graphs - Exercises - Page 27: 7

$ 3x^2+3x\Delta x+(\Delta x)^2 $

$ \frac{f(x+\Delta x)-f(x)}{\Delta x} $ $ \frac{(x+\Delta x)^3-x^3}{\Delta x} $ $ \frac{(x^3+3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3)-x^3}{\Delta x} $ $ \frac{3x^2\Delta x+3x(\Delta x)^2+(\Delta x)^3}{\Delta x} $ $ 3x^2+3x\Delta x+(\Delta x)^2 $