MAT334--2020F > Chapter 1

Question on Textbook Section1.5 The Log Function Example 3

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RunboZhang:
Hi everyone, I have went through textbook section 1.5 and found an example quite confusing (pic is attached below). In this example, in order to get the limit (n->∞), we discuss the real part and imaginary part separately. But I don't know how does it solve for the real part. In particular, it says we need to use L'Hopital's rule and we will get x as the result. However, I have been stuck at this computation (the draft in orange color is my computation) and it seems like a dead end. I dont know if I did wrong at the very first step. Besides, when we are using L'Hopital's rule here, are we taking the derivative with respect to n or x? How can we know which is the variable?

Jessica Long:
The derivative is with respect to n. I've attached my computation of the limit, it starts off in the same way as yours.

Edit: there should be an n2 in the denominator, but it does not affect the result.