Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of -2+1/x-2/x^2
-
Limit of (1+x^3-2*x)/(8+x^10-9*x)
-
Limit of (-2+x)*cot(pi*x)
-
Limit of 10+x^2-7*x
-
Identical expressions
- (- two +x)*cot(pi*x)
- ( minus 2 plus x) multiply by cotangent of ( Pi multiply by x)
- ( minus two plus x) multiply by cotangent of ( Pi multiply by x)
- (-2+x)cot(pix)
- -2+xcotpix
-
Similar expressions
- (-2+x)*cot(pi*x/2)
- (-2-x)*cot(pi*x)
- (2+x)*cot(pi*x)
Limit of the function (-2+x)*cot(pi*x)
The solution
You have entered
[src]
lim ((-2 + x)*cot(pi*x)) x->2+
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
Limit((-2 + x)*cot(pi*x), x, 2)
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 ((-2 + x)*cot(pi*x)) x->2+
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
1 -- pi
$$\frac{1}{\pi}$$
= 0.318309886183791
lim ((-2 + x)*cot(pi*x)) x->2-
$$\lim_{x \to 2^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
1 -- pi
$$\frac{1}{\pi}$$
= 0.318309886183791
= 0.318309886183791
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 2^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \frac{1}{\pi}$$
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \frac{1}{\pi}$$
$$\lim_{x \to \infty}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
More at x→-oo
More at x→2 from the left
$$\lim_{x \to 2^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \frac{1}{\pi}$$
$$\lim_{x \to \infty}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
More at x→oo
$$\lim_{x \to 0^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = \infty$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right) = -\infty$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(\left(x - 2\right) \cot{\left(\pi x \right)}\right)$$
More at x→-oo
The graph