What is #(f(x+h) - f(x))/h# when #f(x) = x^2+9x-3#?

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Answer 1 · 2018-03-05T05:17:44

#=lim_(h->0)((x+h)^2 + 9(x+h) - 3 -( x^2 + 9x - 3))/h#

#=lim_(h->0)(x^2+2xh + h^2 + 9x+ 9h - 3 - x^2 - 9x + 3)/h#

#=lim_(h->0)(cancel(x^2)+2xh + h^2 + cancel(9x)+ 9h - cancel(3) - cancel(x^2) - cancel(9x) + cancel(3))/h#

#=lim_(h->0)(2xh + h^2 + 9h)/h#

#=lim_(h->0)(h(2x + h + 9))/h#

#=lim_(h->0)(cancel(h)(2x + h + 9))/cancel(h)#

#=lim_(h->0)2x + 0 + 9#

= 2x + 9