Question

Find the limit if it exists.

Answer 1

Sorry for the 51.

Explanation:

`\displaystyle \lim_( \Delta x \to 0) \frac { (x+\Delta x)^2 -2* (x+ \Delta x ) +1 -( x^2-2x+1) } {\Delta x} \\\\= \lim_(\Delta x \to 0) \frac { x^2+2*x*\Delta x+\Delta^2 x -2* x-2* \Delta x +1 -( x^2-2x+1) } {\Delta x}\\\\= \lim_(\Delta x \to 0) \frac { 2*x*\Delta x+\Delta^2 x -2* \Delta x } {\Delta x}\\\\\\=2x+0-2\\\\=2x-2\\`