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

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

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

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

0

Solution steps

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

Apply L'Hopital's Rule

: h \to 0 lim (\frac{3 sin ( 3 h )}{1})

= h \to 0 lim (\frac{3 sin ( 3 h )}{1})

Plug in the value

h = 0

= \frac{3 sin ( 3 \cdot 0 )}{1}

Simplify

\frac{3 sin ( 3 \cdot 0 )}{1} : 0

= 0

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