Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (5-4*x+3*x^2)/(1-x+2*x^2)
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Limit of ((1+2*x)/(-1+x))^(4*x)
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Limit of (4+x^2-5*x)/(-16+x^2)
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Limit of sinh(x)/x
- Derivative of:
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cot(x/2)
- Integral of d{x}:
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cot(x/2)
- Graphing y =:
- cot(x/2)
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Identical expressions
- cot(x/ two)
- cotangent of (x divide by 2)
- cotangent of (x divide by two)
- cotx/2
- cot(x divide by 2)
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Similar expressions
- acot(x)/2
- (cot(x)/2)^(1/cos(x))
Limit of the function cot(x/2)
The solution
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[src]
/x\ lim cot|-| x->0+ \2/
$$\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)}$$
Limit(cot(x/2), x, 0)
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
One‐sided limits
[src]
/x\ lim cot|-| x->0+ \2/
$$\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)}$$
oo
$$\infty$$
= 301.998896246434
/x\ lim cot|-| x->0- \2/
$$\lim_{x \to 0^-} \cot{\left(\frac{x}{2} \right)}$$
-oo
$$-\infty$$
= -301.998896246434
= -301.998896246434
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-} \cot{\left(\frac{x}{2} \right)} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)} = \infty$$
$$\lim_{x \to \infty} \cot{\left(\frac{x}{2} \right)} = \cot{\left(\infty \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(\frac{x}{2} \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(\frac{x}{2} \right)} = \infty$$
$$\lim_{x \to \infty} \cot{\left(\frac{x}{2} \right)} = \cot{\left(\infty \right)}$$
More at x→oo
$$\lim_{x \to 1^-} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(\frac{x}{2} \right)} = \frac{1}{\tan{\left(\frac{1}{2} \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(\frac{x}{2} \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
The graph