Question 782297
{{{g(x)=x^2+3x+3}}}


{{{g(5+h)=(5+h)^2+3(5+h)+3}}}


{{{g(5+h)=25+10h+h^2+15+3h+3}}}


{{{g(5+h)=h^2+13h+43}}}


--------------------------------------------------------


{{{g(x)=x^2+3x+3}}}


{{{g(5)=(5)^2+3(5)+3}}}


{{{g(5)=25+15+3}}}


{{{g(5)=43}}}


--------------------------------------------------------


{{{g(5+h)-g(5) = (h^2+13h+43) - (43)}}}


{{{g(5+h)-g(5) = h^2+13h+43 - 43}}}


{{{g(5+h)-g(5) = h^2+13h}}}