Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((-2+x)/(1+x))^(-3+2*x)
-
Limit of (-2*asin(x)+asin(2*x))/x^3
-
Limit of (1/x)^(1/x)
-
Limit of (-2-3*x+2*x^2)/(2+x^2-3*x)
- Derivative of:
-
(1/x)^(1/x)
-
Identical expressions
- (one /x)^(one /x)
- (1 divide by x) to the power of (1 divide by x)
- (one divide by x) to the power of (one divide by x)
- (1/x)(1/x)
- 1/x1/x
- 1/x^1/x
- (1 divide by x)^(1 divide by x)
Limit of the function (1/x)^(1/x)
The solution
You have entered
[src]
___
/ 1
lim x / -
x->oo\/ x
$$\lim_{x \to \infty} \left(\frac{1}{x}\right)^{\frac{1}{x}}$$
Limit((1/x)^(1/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
$$\lim_{x \to \infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
$$\lim_{x \to 0^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the left
$$\lim_{x \to 1^+} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→1 from the right
$$\lim_{x \to -\infty} \left(\frac{1}{x}\right)^{\frac{1}{x}} = 1$$
More at x→-oo
The graph