h → 0

6 + h → 6

secant slope = 6 + h

6

7

5

hole at h = 0

within 1/10
of 6

h within 1/10 of 0

−1

0

1

Squeeze h toward 0 and the slope 6 + h squeezes onto 6. h = 0 itself is a hole; the limit is where the values head: 6.