How do you find the limit of # (1/(h+2)^2 - 1/4) / h# as h approaches 0?

1 Answer
georgef
Mar 17, 2018

We need first to manipulate the expression to put it in a more convenient form

Explanation:

Let's work on the expression

#(1/(h+2)^2 -1/4)/h=((4-(h+2)^2)/(4(h+2)^2)) /h=((4-(h^2+4h+4))/(4(h+2)^2)) /h=(((4-h^2-4h-4))/(4(h+2)^2)) /h=(-h^2-4h)/(4(h+2)^2 h) = (h(-h-4))/(4(h+2)^2 h) = (-h-4)/(4(h+2)^2)#

Taking now limits when #h-> 0# we have:

#lim_(h->0)(-h-4)/(4(h+2)^2) = (-4)/16=-1/4#

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