Question

solve lim(x->0) of (1/(2+x)^2) - 1/4)/x
equation attached, TIA

Answer 1

1/a - 1/b = (b-a)/ab

1/(2+x)^2) - 1/4 = ... ?

Answer 2

\[\lim_{x \rightarrow 0}\frac{ \frac{ 1 }{ \left( 2 + x\right)^{2} } - \frac{ 1 }{ 4 } }{ x }\]

Answer 3

can you simplify the numerator ?

Answer 4

I began by factoring the difference of squares in the numerator

Answer 5

that might not help or it could get complicated

Answer 6

posting how I did it in an image below

Answer 7

\(\dfrac{1}{(x+2)^2} -\dfrac{1}{4} = \dfrac{4- (x+2)^2}{4(x+2)^2}\)
now simplify the numerator of that expression...

Answer 8

can you check my response in the file I posted?

Answer 9

all steps except last one are correct,
\(1\times (-1/4) = -1/4\)

Answer 10

which is the final answer :)