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

The limit as h approaches 0 of ((cos(x+h)-cos(x)))/h is -sin(x)

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

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

- sin (x)

Solution steps

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

Apply L'Hopital's Rule

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

Plug in the value

h = 0

= \frac{- sin ( 0 + x )}{1}

Simplify

= - sin (x)

What is the limit as h approaches 0 of ((cos(x+h)-cos(x)))/h ?
The limit as h approaches 0 of ((cos(x+h)-cos(x)))/h is -sin(x)