I'm having a hard time trying to solve this problem.
\(\displaystyle \lim_{x \rightarrow 1} \frac{x^{2000} - 1}{x-1}\)
I tried factoring the top by using the difference of squares method, but that didn't seem to help with canceling the denominator.
I was thinking that it will cancel and I will end up with something like \(\displaystyle \lim_{x\rightarrow 1}(x^{1,999}+x^{1,998}+x^{1,997}...+1) = 2000\)
Still, assuming this is correct, I'm not sure how I would show my work... At least not without using up the entire page.
Is there another method of solving this? This is from the chapter on derivatives, but aside from using the various forms of difference quotients, we have not been taught any methods like the power rule. So, I don't think I can use that method...
Any help is appreciated.
\(\displaystyle \lim_{x \rightarrow 1} \frac{x^{2000} - 1}{x-1}\)
I tried factoring the top by using the difference of squares method, but that didn't seem to help with canceling the denominator.
I was thinking that it will cancel and I will end up with something like \(\displaystyle \lim_{x\rightarrow 1}(x^{1,999}+x^{1,998}+x^{1,997}...+1) = 2000\)
Still, assuming this is correct, I'm not sure how I would show my work... At least not without using up the entire page.
Is there another method of solving this? This is from the chapter on derivatives, but aside from using the various forms of difference quotients, we have not been taught any methods like the power rule. So, I don't think I can use that method...
Any help is appreciated.
