Mister Exam
Other calculators:
-
How to use it?
- Limit of the function:
-
Limit of ((2+x)/(4+x))^cos(x)
-
Limit of -5-2*x^2+8*x
-
Limit of (-9+x^2)/(-27+x^3)
-
Limit of 1+7*x+11*x^2/2
- Graphing y =:
- -3/x
- Integral of d{x}:
-
-3/x
- Derivative of:
-
-3/x
-
Identical expressions
- - three /x
- minus 3 divide by x
- minus three divide by x
- -3 divide by x
-
Similar expressions
- 3/x
Limit of the function -3/x
The solution
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/-3 \ lim |---| x->oo\ x /
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right)$$
Limit(-3/x, x, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 3 u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right) = 0$$
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right)$$
Let's divide numerator and denominator by x:
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right)$$ =
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right)$$
Do Replacement
$$u = \frac{1}{x}$$
then
$$\lim_{x \to \infty}\left(\frac{\left(-1\right) 3 \frac{1}{x}}{1}\right) = \lim_{u \to 0^+}\left(- 3 u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right) = 0$$
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
$$\lim_{x \to \infty}\left(- \frac{3}{x}\right) = 0$$
$$\lim_{x \to 0^-}\left(- \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{3}{x}\right) = -3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{3}{x}\right) = -3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{3}{x}\right) = 0$$
More at x→-oo
$$\lim_{x \to 0^-}\left(- \frac{3}{x}\right) = \infty$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(- \frac{3}{x}\right) = -\infty$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(- \frac{3}{x}\right) = -3$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(- \frac{3}{x}\right) = -3$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(- \frac{3}{x}\right) = 0$$
More at x→-oo
The graph