lim (cube rt (8+h) - 2) / h h->0
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Think about the definition of the derivative ..
It's supposed to be solved without using L'Hopital. Maybe using rationalization, I don't know...
Originally Posted by sodk It's supposed to be solved without using L'Hopital. Maybe using rationalization, I don't know... Did you see post #2 ?
Or just use good old L`lôpital rule Mmm Latex is strange ^^
Originally Posted by sodk lim (cube rt (8+h) - 2) / h h->0 expanding on Ted's excellent hint ...
Hello, sodk! Here is Ted's suggestion . . . in baby-steps. Recall that: . Find: . Multiply by: . . . . Therefore: .
match up ... to and realize that and the desired limit is the value of ...
Originally Posted by Soroban Hello, sodk! Here is Ted's suggestion . . . in baby-steps. Recall that: . Multiply by: . {h\left[\sqrt[3]{(8+h)^2} + 2\sqrt[3]{8+h} + 4\right]}" alt=" {h\left[\sqrt[3]{(8+h)^2} + 2\sqrt[3]{8+h} + 4\right]}" /> . . . Therefore: . That was exactly what I wanted! Unfortunately your post came late, I've solved it this exact way. My mistake was just trying to rationalize the numerator incorrectly. The trick is the factors Anyway thanks.
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