Question

limit with x approaching 0 at ((1/2+x) (1/2))/x

Answer 1

ts like this

Answer 2

okay dude, assuming that u missed the minus, also I will assume f(x)=1/(2+x)
thus it's derivative at zero is the limit you presented , I mean your limit equals to \[f \prime(x)=\frac{ -1 }{ (x+2 )^2}=\frac{ -1 }{ 4 }\]

Answer 3

here's another more formal solution :\[\lim_{x \rightarrow 0}\frac{ \frac{ 2-(2+x) }{ 2(2+x) } }{ x }=\lim_{x \rightarrow 0}\frac{ -1 }{ 2(2+x) }=\frac{ -1 }{ 4 }\]