Question

lim x tends to 0 1-√1-x^2÷x^2​

Answer 1

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]}