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relationship between two set of variable

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#polynomials #exponential-function #mathematical-modeling
359
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$\sup\{a^{r}\mid r<x; r\in\mathbb{Q}\}=\inf\{a^{s}\mid x<s; s\in\mathbb{Q}\}$ How to prove it?

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#real-analysis #exponential-function
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How to solve exponential function inequality?

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#inequality #exponential-function
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Showing that $e^x > 1+x$

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#calculus #inequality #exponential-function
113
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How to solve this system of ODE's?

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#calculus #ordinary-differential-equations #exponential-function #systems-of-equations
66
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Second order linear ODE not making sense...

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#calculus #ordinary-differential-equations #exponential-function
556
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How to simplify $\cot(\sec^{-1}(e^x))$

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#trigonometry #exponential-function
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How can we describe the graph of $x^x$ for negative values?

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#real-analysis #complex-analysis #graphing-functions #exponential-function
67
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Derivatives of Logarithmic functions

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#calculus #derivatives #exponential-function
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Find the general solution of $\,y'' + 9y = 0$

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#calculus #analysis #ordinary-differential-equations #exponential-function
141
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How to solve $6^{2x}-10\cdot 6^x=-21$ using logarithms?

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#algebra-precalculus #logarithms #exponential-function
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Convergence rate of exponential function

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#functions #convergence-divergence #exponential-function
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Rearranging the terms so that the denominator becomes the numerator

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#algebra-precalculus #exponential-function
74
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Proof of $ e^x-x^2 \gt 1 $ when $ x \gt 0$ and $x$ is a real number .

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#convergence-divergence #exponential-function
119
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$f:\mathbb R \to (0,\infty)$ defined by $f(x)=e^x$. Describe its inverse.

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#functions #exponential-function #inverse

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