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Limit of the function/ 1/t

Limit of the function 1/t

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The solution

You have entered [src] 
     /  1\
 lim |1*-|
t->oo\  t/
lim⁡t→∞(1⋅1t)\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→∞(1⋅1t)\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right)
Let's divide numerator and denominator by t:
lim⁡t→∞(1⋅1t)\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right) =
lim⁡t→∞(11t)\lim_{t \to \infty}\left(\frac{1}{1 t}\right)
Do Replacement
u=1tu = \frac{1}{t}
then
lim⁡t→∞(11t)=lim⁡u→0+u\lim_{t \to \infty}\left(\frac{1}{1 t}\right) = \lim_{u \to 0^+} u
=
0=00 = 0

The final answer:
lim⁡t→∞(1⋅1t)=0\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
02468-8-6-4-2-1010-2020
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits t→0, -oo, +oo, 1
lim⁡t→∞(1⋅1t)=0\lim_{t \to \infty}\left(1 \cdot \frac{1}{t}\right) = 0
lim⁡t→0−(1⋅1t)=−∞\lim_{t \to 0^-}\left(1 \cdot \frac{1}{t}\right) = -\infty
More at t→0 from the left
lim⁡t→0+(1⋅1t)=∞\lim_{t \to 0^+}\left(1 \cdot \frac{1}{t}\right) = \infty
More at t→0 from the right
lim⁡t→1−(1⋅1t)=1\lim_{t \to 1^-}\left(1 \cdot \frac{1}{t}\right) = 1
More at t→1 from the left
lim⁡t→1+(1⋅1t)=1\lim_{t \to 1^+}\left(1 \cdot \frac{1}{t}\right) = 1
More at t→1 from the right
lim⁡t→−∞(1⋅1t)=0\lim_{t \to -\infty}\left(1 \cdot \frac{1}{t}\right) = 0
More at t→-oo
The graph
Limit of the function 1/t
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