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Fungrim entry: 3ac8a5

ex+aexex(ea1)\left|{e}^{x + a} - {e}^{x}\right| \le {e}^{x} \left({e}^{\left|a\right|} - 1\right)
Assumptions:xR  and  aRx \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \in \mathbb{R}
\left|{e}^{x + a} - {e}^{x}\right| \le {e}^{x} \left({e}^{\left|a\right|} - 1\right)

x \in \mathbb{R} \;\mathbin{\operatorname{and}}\; a \in \mathbb{R}
Fungrim symbol Notation Short description
Absz\left|z\right| Absolute value
Expez{e}^{z} Exponential function
RRR\mathbb{R} Real numbers
Source code for this entry:
    Formula(LessEqual(Abs(Sub(Exp(Add(x, a)), Exp(x))), Mul(Exp(x), Sub(Exp(Abs(a)), 1)))),
    Variables(x, a),
    Assumptions(And(Element(x, RR), Element(a, RR))))

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2021-03-15 19:12:00.328586 UTC