Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 7^(1/(-3+x))
-
Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
-
Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
-
Limit of (-6-x^2-3*x+4*x^3)/(3-x^2+2*x^3)
-
Identical expressions
- atan(x)*cot(x)
- arc tangent of gent of (x) multiply by cotangent of (x)
- atan(x)cot(x)
- atanxcotx
-
Similar expressions
- arctan(x)*cot(x)
- arctanx*cot(x)
Limit of the function atan(x)*cot(x)
The solution
You have entered
[src]
lim (atan(x)*cot(x)) x->0+
$$\lim_{x \to 0^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
Limit(atan(x)*cot(x), 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]
lim (atan(x)*cot(x)) x->0+
$$\lim_{x \to 0^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
1
$$1$$
= 1
lim (atan(x)*cot(x)) x->0-
$$\lim_{x \to 0^-}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
1
$$1$$
= 1
= 1
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = 1$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \frac{\pi \cot{\left(1 \right)}}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \frac{\pi \cot{\left(1 \right)}}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = 1$$
$$\lim_{x \to \infty}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
More at x→oo
$$\lim_{x \to 1^-}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \frac{\pi \cot{\left(1 \right)}}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \frac{\pi \cot{\left(1 \right)}}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\cot{\left(x \right)} \operatorname{atan}{\left(x \right)}\right)$$
More at x→-oo
The graph