# How do you find the limit of #(2^w-2)/(w-1)# as w approaches 1?

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To find the limit of (2^w-2)/(w-1) as w approaches 1, we can use L'Hôpital's rule. Taking the derivative of the numerator and denominator separately, we get (ln(2)*2^w)/(1). Evaluating this expression at w=1, we have (ln(2)*2^1)/(1) = ln(2)*2. Therefore, the limit of (2^w-2)/(w-1) as w approaches 1 is ln(2)*2.

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To find the limit of ( \frac{2^w - 2}{w - 1} ) as ( w ) approaches ( 1 ), you can use L'Hôpital's Rule or the property of the derivative of ( 2^w ) at ( w = 1 ). Applying L'Hôpital's Rule, differentiate the numerator and denominator separately with respect to ( w ), then evaluate the limit again. Alternatively, you can rewrite ( 2^w ) as ( e^{w \ln(2)} ), then use the limit definition of the derivative of ( e^x ) at ( x = 0 ). Either method yields the result ( \ln(2) ).

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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.

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