Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of sin(2*x)/(5*x)
-
Limit of ((3+2*x)/(7+5*x))^(1+x)
-
Limit of ((-5+2*x)/(3+2*x))^(7*x)
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Limit of (-6+x+x^2)/(3+x)
- Derivative of:
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2/x
- Integral of d{x}:
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2/x
- Graphing y =:
- 2/x
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Identical expressions
- two /x
- 2 divide by x
- two divide by x
-
Similar expressions
- log(1+3*x^2)/(x^3-5*x^2)
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)
Detail solution
Let's take the limit
$$\lim_{x \to -\infty}\left(\frac{2}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to -\infty}\left(\frac{2}{x}\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(2 u\right)$$
=
$$0 \cdot 2 = 0$$
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:
$$\lim_{x \to -\infty}\left(\frac{2}{x}\right)$$ =
$$\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to -\infty}\left(\frac{2 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(2 u\right)$$
=
$$0 \cdot 2 = 0$$
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
$$\lim_{x \to -\infty}\left(\frac{2}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(\frac{2}{x}\right) = 0$$
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
$$\lim_{x \to 0^-}\left(\frac{2}{x}\right) = -\infty$$
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
The graph