What is the limit as h approaches 0 of 1/h [(1+h)^3-1] ?

The limit as h approaches 0 of 1/h [(1+h)^3-1] is 3

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limit as h approaches 0 of 1/h [(1+h)^3-1]

h \to 0 lim (\frac{1}{h} [(1 + h)^{3} - 1])

3

Solution steps

h \to 0 lim (\frac{1}{h} [(1 + h)^{3} - 1])

Simplify

\frac{1}{h} [(1 + h)^{3} - 1] : h^{2} + 3 h + 3

= h \to 0 lim (h^{2} + 3 h + 3)

Plug in the value

h = 0

= 0^{2} + 3 \cdot 0 + 3

Simplify

= 3

x \to 0 lim (\frac{1}{x ^{\frac{1}{3}}})

x \to 0 + lim (\frac{x}{e ^{- \frac{9}{x}}})

x \to 0 + lim (tan (x^{x}))

x \to 1 lim ((x^{2} - 4) (x - 3))

x \to 0 lim (\frac{2 x}{x + 1})

What is the limit as h approaches 0 of 1/h [(1+h)^3-1] ?
The limit as h approaches 0 of 1/h [(1+h)^3-1] is 3