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How to show $1 - x\le e^{-x} \le \frac{1}{1 + x}$ for $|x| \le 1$

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#calculus #derivatives #inequality #exponential-function #absolute-value
358
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Does natural parameter of exponential family need the constant or sign?

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#statistics #exponential-function #gamma-distribution
123
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Prove $\left(2017^{2018}+2017^{2017}\right)^{2018}>\left(2018^{2017}+2017^{2017}\right)^{2017}$

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#inequality #exponential-function
166
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Prove by Induction that $2^n \geq n+12$ for all $n\geq4$

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#discrete-mathematics #inequality #logic #induction #exponential-function
1.5k
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Parallel Asymptotes

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#exponential-function
2.1k
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Asymptotic growth of factorial and exponential

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#asymptotics #exponential-function #factorial
62
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Exponential linear equations

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#polynomials #exponential-function
709
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Sigmoid Price Elasticity Function Identification

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#calculus #soft-question #exponential-function
68
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Intuition to illustrate is $\lambda^k/k!$

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#calculus #probability #combinatorics #exponential-function #intuition
64
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Prove $ x^{\frac{1}{1-x}} < \frac{1}{e} $ for $ 0 \leq x < 1 $

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#calculus #inequality #proof-writing #exponential-function
314
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function $e^x$ as quotient of two polynomials

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#polynomials #exponential-function #rational-functions
291
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Approximation error of $e - (1+1/x)^x$.

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#real-analysis #limits #exponential-function #approximation #epsilon-delta
69
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What is the co-efficient of $x^2$ in the expansion of $(x+\frac{1}{x^2})^{20}$?

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#combinatorics #exponential-function #binomial-coefficients #fractions #binomial-theorem
59
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Equation for logarithmic and exponential equation

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#logarithms #exponential-function
109
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$ \left( 1 - \frac{x}{n}\right)^n \leq \left( 1 - \frac{x}{n+1}\right)^{n+1} $, $\forall$ $x$ $\in$ $[0,n]$

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#real-analysis #inequality #exponential-function #binomial-theorem #a.m.-g.m.-inequality

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