Question

Evaluate


`lim \: f(x) \: as \: x \: approaches \: 0`
knowing that

`(1)/(2) - {x}^(2) \leqslant 1 - f(x) \leqslant (1)/(2)`
for all instances of x

​

Answer 1

f(0) = 1/2

Explanation:

At x=0, the inequality tells you ...

1/2 ≤ 1 -f(0) ≤ 1/2

That is, ...

1 - f(0) = 1/2

f(0) = 1/2

`\boxed{\lim\limits_(x\to 0){f(x)}=(1)/(2)}`