Mister Exam
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How to use it?
- Limit of the function:
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Limit of (x-sin(x))/(x-tan(x))
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Limit of tanh(n)^(1/n)
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Limit of csch(x)
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Limit of sqrt(2)/2
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Identical expressions
- tanh(n)^(one /n)
- hyperbolic tangent of gent of (n) to the power of (1 divide by n)
- hyperbolic tangent of gent of (n) to the power of (one divide by n)
- tanh(n)(1/n)
- tanhn1/n
- tanhn^1/n
- tanh(n)^(1 divide by n)
Limit of the function tanh(n)^(1/n)
The solution
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n _________ lim \/ tanh(n) n->oo
$$\lim_{n \to \infty} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)}$$
Limit(tanh(n)^(1/n), n, 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 n→0, -oo, +oo, 1
$$\lim_{n \to \infty} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = 1$$
$$\lim_{n \to 0^-} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \tanh{\left(1 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \tanh{\left(1 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = 1$$
More at n→-oo
$$\lim_{n \to 0^-} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \infty$$
More at n→0 from the left
$$\lim_{n \to 0^+} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \tanh{\left(1 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = \tanh{\left(1 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \tanh^{1 \cdot \frac{1}{n}}{\left(n \right)} = 1$$
More at n→-oo
The graph