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15
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Closed Form for $\sum{\frac{x^{n-1}}{n!}}$

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#sequences-and-series #taylor-expansion #exponential-function
91
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What are the minimums of $x^y+y^x$ and $x^y+y^z+z^x$?

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#calculus #optimization #exponential-function #exponentiation #maxima-minima
43
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Integration after differentiation of exponential to exponential

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#integration #derivatives #exponential-function #partial-derivative
88
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Definite Integral of the following term with $e^e$

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#integration #definite-integrals #exponential-function
58
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an elementary inequality in two variables (absolute values and exponentials)

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#inequality #exponential-function #absolute-value
96
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Is it possible to solve $2^{x⁴} + 2^{x² - 1} \le3$ without using derivatives?

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#algebra-precalculus #exponential-function
886
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Minimize the upper bound of a function

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#optimization #exponential-function #upper-lower-bounds
86
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Three Exponential Equations

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#exponential-function
195
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Show that for any integer $n\ge 6$, the inequality $2^n>7n$ holds.

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#algebra-precalculus #inequality #induction #exponential-function #binomial-theorem
902
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Does the Young's inequality $x^2+ y^2\geq 2xy$ hold for negatives $x$ or $y$?

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#algebra-precalculus #inequality #solution-verification #exponential-function
2.5k
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Prove the inequality $0 \leq e^{-nx} - (1-x)^n \leq nx^2 e^{-nx}$ for $x \in [0,1]$ and $n \in \mathbb{N}$.

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#inequality #exponential-function
104
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Integral with exponential (or K-Bessel function) depending on a parameter equal to zero?

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#complex-analysis #definite-integrals #exponential-function #bessel-functions
55
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quick route to the inequality $(x+1)^p \le x^p + 1 + 2^p x (1+x^{p-2})$ for $x \ge 0$ and $p>2$

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#inequality #exponential-function
45
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Is there a logarithm identity that simplifies this expression?

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#logarithms #exponential-function
71
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How I can prove the function $f(t)$ is increasing (decreasing) in $t$?

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#sequences-and-series #logarithms #exponential-function #monotone-functions

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