Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-3+x^2-2*x)/(-3+x)
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Limit of 5^x-cos(x)
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Limit of (x/2)^(1/(-2+x))
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Limit of (1-3/x)^x
- Derivative of:
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cot(2*x)
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Identical expressions
- cot(two *x)
- cotangent of (2 multiply by x)
- cotangent of (two multiply by x)
- cot(2x)
- cot2x
Limit of the function cot(2*x)
The solution
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lim cot(2*x) pi x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)}$$
Limit(cot(2*x), x, pi/4)
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
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lim cot(2*x) pi x->--+ 4
$$\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)}$$
0
$$0$$
= 6.12323399569652e-17
lim cot(2*x) pi x->--- 4
$$\lim_{x \to \frac{\pi}{4}^-} \cot{\left(2 x \right)}$$
0
$$0$$
= 6.12323399577702e-17
= 6.12323399577702e-17
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \frac{\pi}{4}^-} \cot{\left(2 x \right)} = 0$$
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)} = 0$$
$$\lim_{x \to \infty} \cot{\left(2 x \right)} = \cot{\left(\infty \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \cot{\left(2 x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(2 x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(2 x \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
More at x→pi/4 from the left
$$\lim_{x \to \frac{\pi}{4}^+} \cot{\left(2 x \right)} = 0$$
$$\lim_{x \to \infty} \cot{\left(2 x \right)} = \cot{\left(\infty \right)}$$
More at x→oo
$$\lim_{x \to 0^-} \cot{\left(2 x \right)} = -\infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \cot{\left(2 x \right)} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \cot{\left(2 x \right)} = \frac{1}{\tan{\left(2 \right)}}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \cot{\left(2 x \right)} = - \cot{\left(\infty \right)}$$
More at x→-oo
The graph