Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of exp(2*x)
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Limit of 2*x^2
-
Limit of e^(-x)/x
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Limit of x^3-2*x^2
- Integral of d{x}:
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1/t
- Derivative of:
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1/t
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Identical expressions
- one /t
- 1 divide by t
- one divide by t
Limit of the function 1/t
The solution
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/ 1\ lim |1*-| t->oo\ t/
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)$$
Limit(1/t, t, oo, dir='-')
Detail solution
Let's take the limit
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)$$
Let's divide numerator and denominator by t:
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)$$ =
$$\lim_{t \to \infty}\left(\frac{1}{1 t}\right)$$
Do Replacement
$$u = \frac{1}{t}$$
then
$$\lim_{t \to \infty}\left(\frac{1}{1 t}\right) = \lim_{u \to 0^+} u$$
=
$$0 = 0$$
The final answer:
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right) = 0$$
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)$$
Let's divide numerator and denominator by t:
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)$$ =
$$\lim_{t \to \infty}\left(\frac{1}{1 t}\right)$$
Do Replacement
$$u = \frac{1}{t}$$
then
$$\lim_{t \to \infty}\left(\frac{1}{1 t}\right) = \lim_{u \to 0^+} u$$
=
$$0 = 0$$
The final answer:
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right) = 0$$
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 t→0, -oo, +oo, 1
$$\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right) = 0$$
$$\lim_{t \to 0^-}\left(1 \cdot \frac{1}{t}\right) = -\infty$$
More at t→0 from the left
$$\lim_{t \to 0^+}\left(1 \cdot \frac{1}{t}\right) = \infty$$
More at t→0 from the right
$$\lim_{t \to 1^-}\left(1 \cdot \frac{1}{t}\right) = 1$$
More at t→1 from the left
$$\lim_{t \to 1^+}\left(1 \cdot \frac{1}{t}\right) = 1$$
More at t→1 from the right
$$\lim_{t \to -\infty}\left(1 \cdot \frac{1}{t}\right) = 0$$
More at t→-oo
$$\lim_{t \to 0^-}\left(1 \cdot \frac{1}{t}\right) = -\infty$$
More at t→0 from the left
$$\lim_{t \to 0^+}\left(1 \cdot \frac{1}{t}\right) = \infty$$
More at t→0 from the right
$$\lim_{t \to 1^-}\left(1 \cdot \frac{1}{t}\right) = 1$$
More at t→1 from the left
$$\lim_{t \to 1^+}\left(1 \cdot \frac{1}{t}\right) = 1$$
More at t→1 from the right
$$\lim_{t \to -\infty}\left(1 \cdot \frac{1}{t}\right) = 0$$
More at t→-oo
The graph