Can you help me with the steps getting to the right side from the left of the equation.
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$\begingroup$ Why dont you use Mathematica with Debug/Trace turned on? $\endgroup$– WolframFanCommented Jan 11, 2015 at 5:11
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2$\begingroup$ This is just l'Hospital's rule: Take the ratio of the derivative of the numerator and the derivative of the denominator on the left-hand side. $\endgroup$– David G. StorkCommented Jan 11, 2015 at 6:12
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1 Answer
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f[x_] = (1 - 3^(1/x))/(1 + 3^(1/x));
Plot[f[x], {x, -1, 1}, Exclusions -> {x == 0}]
From the documentation for Limit,
Direction -> -1takes variables to approach their limits by decreasing from larger values.
Limit[f[x], x -> 0, Direction -> -1]
-1
Using WolframAlpha from within Mathematica,
WolframAlpha["Limit[(1-3^(1/x))/(1+3^(1/x)), x -> 0, Direction -> -1]",
{{"Limit", 2}, "Content"}, PodStates -> {"Limit__Step-by-step solution"}]
