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tanh(1/x)
Limit of the function/ tanh(1/x)

Limit of the function tanh(1/x)

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You have entered [src] 
         /1\
 lim tanh|-|
x->oo    \x/
lim⁡x→∞tanh⁡(1x)\lim_{x \to \infty} \tanh{\left(\frac{1}{x} \right)} 
Limit(tanh(1/x), x, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-10102-2
Plot the graph
Rapid solution [src] 
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Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞tanh⁡(1x)=0\lim_{x \to \infty} \tanh{\left(\frac{1}{x} \right)} = 0
lim⁡x→0−tanh⁡(1x)=−1\lim_{x \to 0^-} \tanh{\left(\frac{1}{x} \right)} = -1
More at x→0 from the left
lim⁡x→0+tanh⁡(1x)=1\lim_{x \to 0^+} \tanh{\left(\frac{1}{x} \right)} = 1
More at x→0 from the right
lim⁡x→1−tanh⁡(1x)=−1+e21+e2\lim_{x \to 1^-} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}
More at x→1 from the left
lim⁡x→1+tanh⁡(1x)=−1+e21+e2\lim_{x \to 1^+} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}
More at x→1 from the right
lim⁡x→−∞tanh⁡(1x)=0\lim_{x \to -\infty} \tanh{\left(\frac{1}{x} \right)} = 0
More at x→-oo
The graph
Limit of the function tanh(1/x)
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