How do you estimate #(26.8)^(2/3)# using linear approximation?
Charles ArochaSee the answer below:
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Luke AlvarezTo estimate (26.8)^(2/3) using linear approximation, we first find a point near 26.8 where the function is easy to compute. Let's choose 27, as it's a perfect cube. Then, we calculate the derivative of the function f(x) = x^(2/3), which is f'(x) = (2/3) * x^(-1/3). Next, we find the linear approximation of f(x) near x = 27 using the formula f(x) ≈ f(a) + f'(a) * (x - a), where a = 27. Plugging in the values, we get f(x) ≈ (27)^(2/3) + ((2/3) * (27)^(-1/3)) * (x - 27). Simplifying this expression yields the linear approximation. Finally, we substitute 26.8 for x in the linear approximation to get the estimated value.
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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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