Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 10+x^2+3*x^3+8*x
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Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
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Limit of (-4+x^2)/(-3+sqrt(1-4*x))
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Limit of ((1+x)/(-2+x))^(3+x)
- Derivative of:
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cot(1/x)
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Identical expressions
- cot(one /x)
- cotangent of (1 divide by x)
- cotangent of (one divide by x)
- cot1/x
- cot(1 divide by x)
Limit of the function cot(1/x)
The solution
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/1\ lim cot|-| x->oo \x/
$$\lim_{x \to \infty} \cot{\left(\frac{1}{x} \right)}$$
Limit(cot(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
$$\lim_{x \to \infty} \cot{\left(\frac{1}{x} \right)} = \infty$$
$$\lim_{x \to 0^-} \cot{\left(\frac{1}{x} \right)} = - \cot{\left(\infty \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(\frac{1}{x} \right)} = \cot{\left(\infty \right)}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(\frac{1}{x} \right)} = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(\frac{1}{x} \right)} = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(\frac{1}{x} \right)} = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-} \cot{\left(\frac{1}{x} \right)} = - \cot{\left(\infty \right)}$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(\frac{1}{x} \right)} = \cot{\left(\infty \right)}$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(\frac{1}{x} \right)} = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(\frac{1}{x} \right)} = \frac{1}{\tan{\left(1 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(\frac{1}{x} \right)} = -\infty$$
More at x→-oo
The graph