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How can I calculate the remainder of $3^{2012}$ modulo 17?

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#number-theory #modular-arithmetic #exponential-function #factoring
802
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How can I calculate $\lim\limits_{x\rightarrow 0} \frac{(1+x)^{\frac{1}{x}}-e}{x}$?

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#calculus #real-analysis #limits #taylor-expansion #exponential-function
1.1k
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How to find an equation describing mass of sample over time, radioactive decay?

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#linear-algebra #ordinary-differential-equations #exponential-function
60
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$2^{\log_{10}n} = n^{\log_{10}2}$ How are those equal?

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#logarithms #exponential-function
116
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Limit of $n$th root of exponentials

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#real-analysis #limits #exponential-function #limits-without-lhopital
47
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Exponential CDF to a higher power of $X$

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#probability #integration #exponential-function
78
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Limit when $x$ converges to $0$

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#real-analysis #limits #exponential-function #fractions
123
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Limits of power of fractions

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#calculus #real-analysis #analysis #limits #exponential-function
756
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Find the derivative of $y=(\tan (x))^{\log (x)}$

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#calculus #real-analysis #derivatives #logarithms #exponential-function
2.3k
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Why is this not an exponential function?

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#functions #exponential-function
136
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Inequality with powers of 2

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#inequality #exponential-function #integers #substitution #muirhead-inequality
52
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write the inverse of: $y= 3(4)^{2x+1} + 1$

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#exponential-function #inverse
637
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A diophantine equation with unknown exponents: $ 4^n + 5^n = 7^m + 2^m $

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#exponential-function #diophantine-equations #integers
43
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Prove that $|\Phi(p)|^2 \propto\sin^2\left( \frac{p L}{\hbar}\right) $

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#trigonometry #exponential-function #fourier-transform #wave-equation
91
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Finding number of real solution of $4^x-2^{2+x}\cos(e^x)+1=0$

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#calculus #real-analysis #trigonometry #logarithms #exponential-function

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