Mister Exam
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- Limit of the function:
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Limit of sin(5*x)/(2*x)
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Limit of (-9+x^2)/(-3+x^2-2*x)
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Limit of sin(3*x)/(4*x)
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Limit of cosh(x)
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Identical expressions
- coth(one /x)
- hyperbolic co tangent of gent of (1 divide by x)
- hyperbolic co tangent of gent of (one divide by x)
- coth1/x
- coth(1 divide by x)
Limit of the function coth(1/x)
The solution
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/1\ lim coth|-| x->oo \x/
$$\lim_{x \to \infty} \coth{\left(\frac{1}{x} \right)}$$
Limit(coth(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
$$\lim_{x \to \infty} \coth{\left(\frac{1}{x} \right)} = \infty$$
$$\lim_{x \to 0^-} \coth{\left(\frac{1}{x} \right)} = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \coth{\left(\frac{1}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \coth{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{-1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \coth{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{-1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \coth{\left(\frac{1}{x} \right)} = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-} \coth{\left(\frac{1}{x} \right)} = -1$$
More at x→0 from the left
$$\lim_{x \to 0^+} \coth{\left(\frac{1}{x} \right)} = 1$$
More at x→0 from the right
$$\lim_{x \to 1^-} \coth{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{-1 + e^{2}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \coth{\left(\frac{1}{x} \right)} = \frac{1 + e^{2}}{-1 + e^{2}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \coth{\left(\frac{1}{x} \right)} = -\infty$$
More at x→-oo
The graph