Let f(x)= lim as h->0 of ((x+h)^2-x^2)/ h. For what value of x does f(x)= 4?

Answer 1

(x+h)^2-x^2 = x^2 + 2 x h + h^2 - x^2
or in other words 2 x h + h^2
or h (2 x + h)
divide that by h
2x+h
limit as h ---> 0 is
2 x
so
f(x) = 2 x as h--->0
4 = 2 x
x = 2