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Exponential equations

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#exponential-function
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Calculate the matrices $[{A{π \over 4}]}^v$ for all possible values of v

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#matrices #exponential-function
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Solving an exponential equation that includes division and multiplication

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#exponential-function
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Exponential equation with fractions

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#exponential-function
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Is it possible to figure out the coefficients of an exponential equation given a certain number of points?

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#exponential-function
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Forming differential equation

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#ordinary-differential-equations #exponential-function
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Show that $\int x\mathrm{e}^{-\alpha x^2}\mathrm dx =\dfrac{-1}{2\alpha} \mathrm e^{-\alpha x^2}$ + Constant

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#integration #definite-integrals #exponential-function #intuition
349
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Show that the standard integral: $\int_{0}^{\infty} x^4\mathrm{e}^{-\alpha x^2}\mathrm dx =\frac{3}{8}{\left(\frac{\pi}{\alpha^5}\right)}^\frac{1}{2}$

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#integration #definite-integrals #exponential-function #function-and-relation-composition
301
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Partial sum of exponential series strictly increases after certain step

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#sequences-and-series #inequality #exponential-function
156
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When does $\exp\left(\sum_{i=1}^\infty a_i\right)=\prod_{i=1}^\infty \exp(a_i) ?$

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#complex-analysis #analysis #limits #exponential-function
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Exponential Derivative Word Problem

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#calculus #derivatives #exponential-function
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"Time until arrival/departure" in a Poisson process...

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#probability #exponential-function #poisson-distribution
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Singularity type of $\frac{1}{z} e^{-\frac{1}{z^2}} $

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#complex-analysis #exponential-function #laurent-series
373
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Generalized Trigonometric Functions in terms of exponentials and roots of unity

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#complex-analysis #trigonometry #special-functions #exponential-function
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Evaluating a limit I

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#calculus #limits #exponential-function

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