- #1
nycmathdad
- 74
- 0
Use the Squeeze Theorem to find the limit.
lim (x^2 • sin(1/x))
x--> 0
Let me see.
-1 ≤ sin (1/x) ≤ 1
-x^2 ≤ x^2 • sin(1/x) ≤ x^2
-|x^2| ≤ x^2 • sin(1/x) ≤ |x^2|
lim -|x^2| as x tends to 0 = 0.
lim |x^2| as x tends to 0 = 0.
.
By the Squeeze Theorem, x^2 • sin(1/x) was squeezed between the limit of -|x^2| as x tends to 0 and the limit of |x^2| as x tends to 0.
Conclusion:
lim (x^2 • sin(1/x)) = 0
x--> 0
The limit is 0.
Correct?
lim (x^2 • sin(1/x))
x--> 0
Let me see.
-1 ≤ sin (1/x) ≤ 1
-x^2 ≤ x^2 • sin(1/x) ≤ x^2
-|x^2| ≤ x^2 • sin(1/x) ≤ |x^2|
lim -|x^2| as x tends to 0 = 0.
lim |x^2| as x tends to 0 = 0.
.
By the Squeeze Theorem, x^2 • sin(1/x) was squeezed between the limit of -|x^2| as x tends to 0 and the limit of |x^2| as x tends to 0.
Conclusion:
lim (x^2 • sin(1/x)) = 0
x--> 0
The limit is 0.
Correct?