Suppose x : [0,∞) → [0,∞) is continuous and x(0) = 0. If
\(x(t)\le2+\int_0^tx(s)ds,for \;all\:t\ge 0\), for all t ≥ 0,
then which of the following is true?
(a) x( √ 2) ∈ [0, 2]
(b) x( √ 2) ∈ [0, \(2e^\sqrt2\)]
(c) x( √ 2) ∈ [\(\frac{5}{\sqrt2},\frac{7}{\sqrt2}\)]
(d) x( √ 2) ∈ [10,∞)
- Voclasses