How do you find the derivative using limits of #g(x)=-5#?
The derivative of a constant is null. In fact using the definition of derivative:
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To find the derivative of a constant function ( g(x) = -5 ), you apply the definition of the derivative:
[ \lim_{h \to 0} \frac{g(x + h) - g(x)}{h} ]
For ( g(x) = -5 ), the function remains constant regardless of the value of ( x ). Therefore, ( g(x + h) = -5 ) and ( g(x) = -5 ). Substituting these values into the limit expression, we get:
[ \lim_{h \to 0} \frac{-5 - (-5)}{h} = \lim_{h \to 0} \frac{0}{h} = 0 ]
Hence, the derivative of ( g(x) = -5 ) with respect to ( x ) is ( 0 ).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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