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

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

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

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

3

Solution steps

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

Simplify

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

f (x) = \frac{1 - 2 x}{3 - x}

\frac{d}{d x} (x + 7)

\int [6 cos (x) - 2 sec (x) tan (x)] d x

\int sec (u) tan (u) d u

x \to 7 + lim (\frac{∣ x - 7 ∣}{x - 7})

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