How do you find the derivative using limits of #f(x)=1/(x-1)#?
Please see the explanation.
Find f'(x)
Multiply numerators and denominators:
The second term in the numerator becomes 1:
Multiply numerators and denominators:
I shall mark what cancels:
Remove the canceled factors:
Distribute the -1 in the numerator:
Combine like terms in the numerator:
Simplify:
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To find the derivative of ( f(x) = \frac{1}{x - 1} ) using limits, you apply the definition of the derivative:
[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]
Substitute ( f(x) = \frac{1}{x - 1} ) into the formula and simplify.
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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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