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

The limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h is 1/2

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limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h

h \to 0 lim (\frac{sin ( \frac{π}{3} + h ) - sin ( \frac{π}{3} )}{h})

\frac{1}{2}

Decimal Notation

0.5

Solution steps

h \to 0 lim (\frac{sin ( \frac{π}{3} + h ) - sin ( \frac{π}{3} )}{h})

Apply L'Hopital's Rule

: h \to 0 lim (\frac{cos ( h + \frac{π}{3} )}{1})

= h \to 0 lim (\frac{cos ( h + \frac{π}{3} )}{1})

Plug in the value

h = 0

= \frac{cos ( 0 + \frac{π}{3} )}{1}

Simplify

\frac{cos ( 0 + \frac{π}{3} )}{1} : \frac{1}{2}

= \frac{1}{2}

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What is the limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h ?
The limit as h approaches 0 of (sin(pi/3+h)-sin(pi/3))/h is 1/2