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- Limit of the function:
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Limit of tanh(1/x)
- Limit of (x^4-a^4)/(x-a)
- Limit of 1/factorial(n)
- Limit of factorial(n)
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Identical expressions
- tanh(one /x)
- hyperbolic tangent of gent of (1 divide by x)
- hyperbolic tangent of gent of (one divide by x)
- tanh1/x
- tanh(1 divide by x)
Limit of the function tanh(1/x)
The solution
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/1\ lim tanh|-| x->oo \x/
$$\lim_{x \to \infty} \tanh{\left(\frac{1}{x} \right)}$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty} \tanh{\left(\frac{1}{x} \right)} = 0$$
$$\lim_{x \to 0^-} \tanh{\left(\frac{1}{x} \right)} = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \tanh{\left(\frac{1}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \tanh{\left(\frac{1}{x} \right)} = 0$$
More at x→-oo
$$\lim_{x \to 0^-} \tanh{\left(\frac{1}{x} \right)} = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \tanh{\left(\frac{1}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \tanh{\left(\frac{1}{x} \right)} = \frac{-1 + e^{2}}{1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \tanh{\left(\frac{1}{x} \right)} = 0$$
More at x→-oo
The graph