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Taylor series of f(x + a) becomes exponential

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#taylor-expansion #exponential-function
129
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Evaluating $\lim_{x\to 0} x^x$

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#limits #exponential-function
138
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Linearizing an expression involving exponentials

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#calculus #real-analysis #exponential-function
122
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Proving that $3^n<n!$ when $n\geq 7$

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#algebra-precalculus #induction #exponential-function #factorial
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Find when the population is growing the fastest, under the logistic model

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#calculus #derivatives #logarithms #exponential-function
171
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$\pi$ base $e$ or $\pi=\sum\limits_{n=-1}^{\infty} a_ne^{-n}$ where $a_n\in\{0,1,-1\}$

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#power-series #exponential-function #pi #number-systems
68
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Is it possible to find the value of $x$ where $e^x$ exceeds $x^{10}$ by hand?

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#functions #polynomials #exponential-function
30
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Computing efficiently a small base to the power a large number

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#algorithms #exponential-function
99
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Why wolfram alpha find no solution to $x^\frac13= -1$?

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#exponential-function #wolfram-alpha
69
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Exponent - Solving for an unknown within an expectation

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#probability #random-variables #normal-distribution #exponential-function
2.2k
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Zeroes of sin(x)

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#complex-analysis #trigonometry #complex-numbers #exponential-function #roots
49
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Find range of the given function : $ f(x) = \frac{e^x}{1+ \lceil x\rceil } $ when $ x \ge 0 $

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#functions #exponential-function
90
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Population ratio of Birth control to no birth control

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#exponential-function
76
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Troubles understanding this limit

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#real-analysis #limits #exponential-function #limits-without-lhopital
3.2k
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Prove that $ex \leq e^x$ for all $x \in \mathbb{R}$

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#real-analysis #inequality #exponential-function

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