for-a-gt-b-gt-0-show-that-b-lt-ax-x-bx-x-e-x-e-x-lt-a-

Question Number 128731 by TITA last updated on 09/Jan/21

for a > b > 0 show that

b < \frac{{ax}^{x} + {bx}^{- x}}{e^{x} + e^{- x}} < a

Commented by TITA last updated on 09/Jan/21

please help

Commented by MJS_new last updated on 09/Jan/21

{it}^{'} s not true if we are free to choose x \in R^{+}

i . e .

b = 1 \land a = 2

1 < \frac{2 x^{x} + x^{- x}}{e^{x} + e^{- x}} < 2 \Leftrightarrow 0 < x <\approx . 937325 \lor \approx 1.83623 < x <\approx 2.72045

not true for all other values of x

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