lim x tends to 0 1-√1-x^2÷x^2
Answers
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0
Step-by-step explanation:
Explanation:
It is easily shown, that, as
x
gets smaller,
x
2
gets smaller at an even greater rate, so
1
x
2
will be greater.
A few steps:
x
=
1
→
x
2
=
1
→
1
x
2
=
1
x
=
1
2
→
x
2
=
1
4
→
1
x
2
=
4
x
=
1
100
→
x
2
=
10000
→
1
x
2
=
10000
This means that the closer
x
goes to
0
the higher the function goes. In this case it doesn't matter whether
x
→
0
from the positive side or from the negative, as the square makes it al positive. By choosing smaller and smaller values of
x
, the function can reach any size you want.
Translated to "the language":
lim
x
→
0
+
1
x
2
=
lim
x
→
0
−
1
x
2
=
lim
x
→
0
1
x
2
=
∞
graph{1/x^2 [-17.75, 18.3, -1.61, 16.42]}
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