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Fungrim entry: 02751f

x+axx(11ax)\left|\sqrt{x + a} - \sqrt{x}\right| \le \sqrt{x} \left(1 - \sqrt{1 - \frac{\left|a\right|}{x}}\right)
Assumptions:x(0,)  and  aR  and  axx \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left|a\right| \le x
\left|\sqrt{x + a} - \sqrt{x}\right| \le \sqrt{x} \left(1 - \sqrt{1 - \frac{\left|a\right|}{x}}\right)

x \in \left(0, \infty\right) \;\mathbin{\operatorname{and}}\; a \in \mathbb{R} \;\mathbin{\operatorname{and}}\; \left|a\right| \le x
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Sqrtz\sqrt{z} Principal square root
OpenInterval(a,b)\left(a, b\right) Open interval
Infinity\infty Positive infinity
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(LessEqual(Abs(Sub(Sqrt(Add(x, a)), Sqrt(x))), Mul(Sqrt(x), Sub(1, Sqrt(Sub(1, Div(Abs(a), x))))))),
    Variables(x, a),
    Assumptions(And(Element(x, OpenInterval(0, Infinity)), Element(a, RR), LessEqual(Abs(a), x))))

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2021-03-15 19:12:00.328586 UTC