10.lim h-->0 (x+h)²-x²/ h h-->0

Question

1. lim (x+h)²-x²/ h

h-->0

Answer 1

f'(x) = lim_h→0 [f(x+h) - f(x)] / h

So, if f(x) = x², then the value of the given limit is f'(x), which is 2x.

Answer 2

1. lim (x+h)²-x²/ h = lim (2xh + h²/ h = lim(2x + h) = 2x = f'(x).

h-->0 h-->0 h-->0

Answer: 2x

This