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