Question

lim of ((-5+h)^2-25)/(h) as x approaches 0


Can someone explain to me step by step how this equals -10...??

Answer 1

\[\frac{ (-5+h)^{2}-25 }{ h }=\frac{ 25-10h+h^{2}-25 }{ h }=-10+h\]

Answer 2

well start with writing it correctly

\[\lim_{h \rightarrow 0}\frac{( -5 + h)^2 - 25}{h}\]

simplify the numerator

\[\lim_{h \rightarrow 0}\frac{25 - 10h + h^2 - 25}{h} = \lim_{h \rightarrow 0}\frac{-10h + h^2}{h}\]

remove to common factor

\[\lim_{h \rightarrow 0} \frac{h(-10 + h)}{h} =\lim_{h \rightarrow 0} -10 + h\]

now substitute h = 0 into the limit

-10 + 0 = -10

Answer 3

Thanks guys! that helped a lot... i think i forgot to simplify and instead went right ahead and plugged in the 0 giving me a DNE