University⏱ 3 min

Limit

What approaching a value means

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L = 1f(x) ≈ 0.9585

The more you zoom in, the closer the points get to zero - and the closer f(x) gets to 1.

From both sides

f(−0.502)0.95846
f(+0.502)0.95846
gap from 10.04154
lim⁡x o0\ racsin⁡xx=1\lim_{x \ o 0} \ rac{\sin x}{x} = 1

At x = 0 the function does not exist (open circle) - you cannot divide by zero. But as we approach from both sides, f(x) gets closer and closer to 1 and the gap shrinks to zero. That target value is the limit.