Find the limits: lim h➡0 (1+h)^3-1/hneed to show work
1 answer:
9514 1404 393
Answer:
3
Step-by-step explanation:
The expression can be simplified and then evaluated at h=0.
((1 +h)^3 -1)/h = (1 +3h +3h^2 +h^3 -1)/h
= (3h +3h^2 +h^3)/h
= 3 +3h +h^2
This evaluates to 3 when h=0.
The limit of interest is 3.
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Strictly speaking, the simplified form is only valid when h ≠ 0. However, that form is useful for finding the limit.
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