Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of (5-4*x+3*x^2)/(1-x+2*x^2)
-
Limit of ((1+2*x)/(-1+x))^(4*x)
-
Limit of (4+x^2-5*x)/(-16+x^2)
-
Limit of sinh(x)/x
- Integral of d{x}:
-
-2/x
- Graphing y =:
- -2/x
- Derivative of:
-
-2/x
-
Identical expressions
- - two /x
- minus 2 divide by x
- minus two divide by x
- -2 divide by x
-
Similar expressions
- 2/x
Limit of the function -2/x
The solution
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/-2 \ lim |---| x->oo\ x /
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right)$$
Limit(-2/x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 2 u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 2 u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right) = 0$$
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
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(- \frac{2}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(- \frac{2}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{2}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{2}{x}\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{2}{x}\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{2}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- \frac{2}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{2}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{2}{x}\right) = -2$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{2}{x}\right) = -2$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{2}{x}\right) = 0$$
More at x→-oo
The graph