What is the limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h ?

The limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h is -(sqrt(2))/2

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limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h

h \to 0 lim (\frac{cos ( \frac{π}{4} + h ) - cos ( \frac{π}{4} )}{h})

- \frac{2}{2}

Decimal

- 0.70710 \dots

Solution steps

h \to 0 lim (\frac{cos ( \frac{π}{4} + h ) - cos ( \frac{π}{4} )}{h})

Apply L'Hopital's Rule

= h \to 0 lim (\frac{- sin ( h + \frac{π}{4} )}{1})

Plug in the value

h = 0

= \frac{- sin ( 0 + \frac{π}{4} )}{1}

Simplify

\frac{- sin ( 0 + \frac{π}{4} )}{1} : - \frac{2}{2}

= - \frac{2}{2}

What is the limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h ?
The limit as h approaches 0 of (cos(pi/4+h)-cos(pi/4))/h is -(sqrt(2))/2