What is the limit as h approaches 0 of (sin(7h))/h ?

The limit as h approaches 0 of (sin(7h))/h is 7

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limit as h approaches 0 of (sin(7h))/h

h \to 0 lim (\frac{sin ( 7 h )}{h})

7

Solution steps

h \to 0 lim (\frac{sin ( 7 h )}{h})

Apply L'Hopital's Rule

: h \to 0 lim (\frac{cos ( 7 h ) \cdot 7}{1})

= h \to 0 lim (\frac{cos ( 7 h ) \cdot 7}{1})

Plug in the value

h = 0

= \frac{cos ( 7 \cdot 0 ) \cdot 7}{1}

Simplify

\frac{cos ( 7 \cdot 0 ) \cdot 7}{1} : 7

= 7

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What is the limit as h approaches 0 of (sin(7h))/h ?
The limit as h approaches 0 of (sin(7h))/h is 7