Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of 1/(-1+2*n)
-
Limit of (1+x)^3+(-1+x)^2-(-1+x)^3/(1+x)^2
-
Limit of tan(5*x)/tan(4*x)
-
Limit of sqrt((1+x)/x)
- Graphing y =:
- sqrt((1+x)/x)
-
Identical expressions
- sqrt((one +x)/x)
- square root of ((1 plus x) divide by x)
- square root of ((one plus x) divide by x)
- √((1+x)/x)
- sqrt1+x/x
- sqrt((1+x) divide by x)
-
Similar expressions
- ((1+x)^(1/3)-sqrt(1+x))/x
- -1/x+sqrt(1+x)/x
- sqrt((1-x)/x)
- sqrt(1+x)/x-sqrt(1-x)/x
- (-6+6*sqrt(1+x))/x
Limit of the function sqrt((1+x)/x)
The solution
You have entered
[src]
_______
/ 1 + x
lim / -----
x->oo\/ x
$$\lim_{x \to \infty} \sqrt{\frac{x + 1}{x}}$$
Limit(sqrt((1 + x)/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
$$\lim_{x \to \infty} \sqrt{\frac{x + 1}{x}} = 1$$
$$\lim_{x \to 0^-} \sqrt{\frac{x + 1}{x}} = \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{\frac{x + 1}{x}} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{\frac{x + 1}{x}} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{\frac{x + 1}{x}} = 1$$
More at x→-oo
$$\lim_{x \to 0^-} \sqrt{\frac{x + 1}{x}} = \infty i$$
More at x→0 from the left
$$\lim_{x \to 0^+} \sqrt{\frac{x + 1}{x}} = \infty$$
More at x→0 from the right
$$\lim_{x \to 1^-} \sqrt{\frac{x + 1}{x}} = \sqrt{2}$$
More at x→1 from the left
$$\lim_{x \to 1^+} \sqrt{\frac{x + 1}{x}} = \sqrt{2}$$
More at x→1 from the right
$$\lim_{x \to -\infty} \sqrt{\frac{x + 1}{x}} = 1$$
More at x→-oo
The graph