Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
-
Limit of ((-4+3*x)/(2+3*x))^(1+x)/3
-
Limit of (-16+2^x)/(-1+5*sqrt(x)*(5-x))
-
Limit of (-14+x^2-5*x)/(-6+x+2*x^2)
-
Limit of (3+x^2+4*x)/(1+x^3)
- Integral of d{x}:
-
-1/y
- Derivative of:
-
-1/y
-
Identical expressions
- - one /y
- minus 1 divide by y
- minus one divide by y
- -1 divide by y
-
Similar expressions
- 1/y
Limit of the function -1/y
The solution
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/-1 \ lim |---| y->oo\ y /
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right)$$
Limit(-1/y, y, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right)$$
Let's divide numerator and denominator by y:
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right)$$ =
$$\lim_{y \to \infty}\left(\frac{\left(-1\right) \frac{1}{y}}{1}\right)$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty}\left(\frac{\left(-1\right) \frac{1}{y}}{1}\right) = \lim_{u \to 0^+}\left(- u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right) = 0$$
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right)$$
Let's divide numerator and denominator by y:
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right)$$ =
$$\lim_{y \to \infty}\left(\frac{\left(-1\right) \frac{1}{y}}{1}\right)$$
Do Replacement
$$u = \frac{1}{y}$$
then
$$\lim_{y \to \infty}\left(\frac{\left(-1\right) \frac{1}{y}}{1}\right) = \lim_{u \to 0^+}\left(- u\right)$$
=
$$- 0 = 0$$
The final answer:
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right) = 0$$
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 y→0, -oo, +oo, 1
$$\lim_{y \to \infty}\left(- \frac{1}{y}\right) = 0$$
$$\lim_{y \to 0^-}\left(- \frac{1}{y}\right) = \infty$$
More at y→0 from the left
$$\lim_{y \to 0^+}\left(- \frac{1}{y}\right) = -\infty$$
More at y→0 from the right
$$\lim_{y \to 1^-}\left(- \frac{1}{y}\right) = -1$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(- \frac{1}{y}\right) = -1$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(- \frac{1}{y}\right) = 0$$
More at y→-oo
$$\lim_{y \to 0^-}\left(- \frac{1}{y}\right) = \infty$$
More at y→0 from the left
$$\lim_{y \to 0^+}\left(- \frac{1}{y}\right) = -\infty$$
More at y→0 from the right
$$\lim_{y \to 1^-}\left(- \frac{1}{y}\right) = -1$$
More at y→1 from the left
$$\lim_{y \to 1^+}\left(- \frac{1}{y}\right) = -1$$
More at y→1 from the right
$$\lim_{y \to -\infty}\left(- \frac{1}{y}\right) = 0$$
More at y→-oo
The graph