2h is incorrect

you shouldsimplify like so:

lim h->0 [2(x+h)^2 +3 -(2(x)^2+3)] / h =

lim h->0 2(x^2+2xh+h^2)+3-2x^2 -3 / h =

lim h->0 2x^2+4xh+2h^2-2x^2 / h=

lim h->0 4xh+2h^2 / h =

lim h->0 h(4x+2h) /h=

lim h->0 4x + 2h=

4x +2(0)=

4x (which is the derivative)

but since no limits are mentioned it would be 4x +2h

(2x^2 + 4xh + 2h^2 + 3 - 2x^2 - 3) / h

=(4xh + 2h^2)/h

=4x + 2h

f(x)=a million/(3x) f(x+h) = a million / [3(x+h)] permit's replace into the difference quotient formula: [ f(x+h) - f(x) ] / h ..... [a million / 3*(x +h) ] - [a million/(3x)] =------------------------------- ............. h multiply the numerator and the denominator by using the liquid crystal demonstrate=3(x+h)(x) (to get rid off the fractions. .......{ [a million / 3*(x +h)] - [a million/(3x)]} * [3(x+h)(x)] =-------------------------------------... .............. h * 3(x+h)(x) .... x - (x +h) =--------------------- ......h * 3(x+h)(x) distribute the -a million into the parenthesis interior the numerator, and combine like words .... x - x -h =--------------------- ......h * 3(x+h)(x) ........... -h =--------------------- ......h * 3(x+h)(x) you are able to now simplify the fraction by using canceling an h ........... -a million =--------------------- ...... (3x+3h)*(x)