Calcule \lim _{x\to \:3}\left(\frac{x^{2000}-3^{2000}}{x-3}\right). Como esse limite se relaciona com uma derivada?

Acredito que seja para relacionar f'\left(x\right)=\lim _{\Delta x\to 0}\:\frac{f\left(\Delta x+x_1\right)-f\left(x_1\right)}{\Delta x}com o conceito de derivada:


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