# How do you find the derivative of #f(x) = x+3# using the limit definition?

Applying the limit definition of the derivative , we have:

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To find the derivative of ( f(x) = x + 3 ) using the limit definition:

[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

Substitute ( f(x) = x + 3 ):

[ f'(x) = \lim_{h \to 0} \frac{(x + h + 3) - (x + 3)}{h} ]

[ f'(x) = \lim_{h \to 0} \frac{x + h + 3 - x - 3}{h} ]

[ f'(x) = \lim_{h \to 0} \frac{h}{h} ]

[ f'(x) = \lim_{h \to 0} 1 ]

[ f'(x) = 1 ]

Therefore, the derivative of ( f(x) = x + 3 ) with respect to ( x ) is ( 1 ).

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