Mister Exam
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How to use it?
- Limit of the function:
- Limit of factorial(n)
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Limit of cosh(1/x)
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Limit of factorial(x)/(1+2*x)
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Limit of 20
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Identical expressions
- cosh(one /x)
- hyperbolic co sinus of e of ine of (1 divide by x)
- hyperbolic co sinus of e of ine of (one divide by x)
- cosh1/x
- cosh(1 divide by x)
Limit of the function cosh(1/x)
The solution
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/ 1\ lim cosh|1*-| x->oo \ x/
$$\lim_{x \to \infty} \cosh{\left(1 \cdot \frac{1}{x} \right)}$$
Limit(cosh(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
$$\lim_{x \to \infty} \cosh{\left(1 \cdot \frac{1}{x} \right)} = 1$$
$$\lim_{x \to 0^-} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \cosh{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \cosh{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cosh{\left(1 \cdot \frac{1}{x} \right)} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \cosh{\left(1 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cosh{\left(1 \cdot \frac{1}{x} \right)} = \cosh{\left(1 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cosh{\left(1 \cdot \frac{1}{x} \right)} = 1$$
More at x→-oo
The graph