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Results tagged with real-analysis
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user 128393
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
3
votes
1
answer
260
views
How to prove that the following function is monotonically increasing?
$$f(x) = \frac{\sqrt{x}\int_a^1 e^{-xs} s^{b+1}~ \mathrm{d}s}{\int_a^1 e^{-xs} s^{b} ~\mathrm{d}s}:\left]0,+\infty\right[\ \to \mathbb{R} $$
where $0 < a < 1$ and $b > 0.$
By applying elementary ru …
- 231
0
votes
1
answer
102
views
How to prove that the following function is monotonically decreasing?
$f(x) = \frac{\int_{\alpha x}^{x} e^{-t} t^{b+1}\ dt}{x \int_{\alpha x}^{x} e^{-t} t^b\ dt}:\ ]\ 0,+\infty\ [\ \to \mathbb{R}$
where $\ 0<\alpha<1\ $ and $\ b>0$
- 231
10
votes
1
answer
3k
views
Can the supremum of continuous functions be discontinuous at every point of an interval?
Pether Luthy gave an example of a sequence of continuous real valued functions whose supremum was discontinuous on a set of positive measure. But does it exist a sequence of continuous real valued fun …
- 231