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Fungrim entry: 3ac8a5

∣ex+a−ex∣≤ex(e∣a∣−1)\left|{e}^{x + a} - {e}^{x}\right| \le {e}^{x} \left({e}^{\left|a\right|} - 1\right)
Assumptions:x∈R and⁡ a∈Rx \in \mathbb{R} \,\mathbin{\operatorname{and}}\, a \in \mathbb{R}
TeX:
\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}
Definitions:
Fungrim symbol Notation Short description
Abs∣z∣\left|z\right| Absolute value
Expez{e}^{z} Exponential function
RRR\mathbb{R} Real numbers
Source code for this entry:
Entry(ID("3ac8a5"),
    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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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-06-18 07:49:59.356594 UTC