Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (-1+x)/(x+x^2)
-
Limit of log(-5+x)/log(e^x-e^5)
-
Limit of (-exp(-x)-2*x+exp(x))/(x-sin(x))
- Limit of e^(-n*x)/n
- Graphing y =:
- x+1/x
- Canonical form:
- x+1/x
- Integral of d{x}:
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x+1/x
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Identical expressions
- x+ one /x
- x plus 1 divide by x
- x plus one divide by x
- x+1 divide by x
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Similar expressions
- x-1/x
Limit of the function x+1/x
The solution
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[src]
/ 1\ lim |x + -| x->0+\ x/
$$\lim_{x \to 0^+}\left(x + \frac{1}{x}\right)$$
Limit(x + 1/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]
/ 1\ lim |x + -| x->0+\ x/
$$\lim_{x \to 0^+}\left(x + \frac{1}{x}\right)$$
oo
$$\infty$$
= 151.006622516556
/ 1\ lim |x + -| x->0-\ x/
$$\lim_{x \to 0^-}\left(x + \frac{1}{x}\right)$$
-oo
$$-\infty$$
= -151.006622516556
= -151.006622516556
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 0^-}\left(x + \frac{1}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + \frac{1}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(x + \frac{1}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x + \frac{1}{x}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + \frac{1}{x}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + \frac{1}{x}\right) = -\infty$$
More at x→-oo
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x + \frac{1}{x}\right) = \infty$$
$$\lim_{x \to \infty}\left(x + \frac{1}{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 1^-}\left(x + \frac{1}{x}\right) = 2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x + \frac{1}{x}\right) = 2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x + \frac{1}{x}\right) = -\infty$$
More at x→-oo
The graph