Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-6+x^2-x)/(6+x^2-5*x)
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Limit of log(1+x^2)/(-e^(-x)+cos(3*x))
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Limit of -2+|-2+x|/x
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Limit of (-4-8*x+8*x^2)/(3+8*x)
- Graphing y =:
- cot(5*x)
- Derivative of:
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cot(5*x)
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Identical expressions
- cot(five *x)
- cotangent of (5 multiply by x)
- cotangent of (five multiply by x)
- cot(5x)
- cot5x
Limit of the function cot(5*x)
The solution
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lim cot(5*x) x->oo
$$\lim_{x \to \infty} \cot{\left(5 x \right)}$$
Limit(cot(5*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
$$\lim_{x \to \infty} \cot{\left(5 x \right)} = \cot{\left(\infty \right)}$$
$$\lim_{x \to 0^-} \cot{\left(5 x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(5 x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(5 x \right)} = \frac{1}{\tan{\left(5 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(5 x \right)} = \frac{1}{\tan{\left(5 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(5 x \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
$$\lim_{x \to 0^-} \cot{\left(5 x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(5 x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(5 x \right)} = \frac{1}{\tan{\left(5 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(5 x \right)} = \frac{1}{\tan{\left(5 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(5 x \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
The graph