calculus - This is very easy but i am struck with one

Question

This is findind limit calculus one. This would be very easy but i never factor high degrees. can anyone show me how to factor it.

lim((x^5-32)/(x-2),x=2)

lim((x^5-2^5)/(x-2),x=2)

Answer 1

正如约翰在上面的评论中所建议的那样：当 x-->2 我们处理 0/0 类型的限制时。为了计算它，我们使用分子的导数和分母的导数：

f'(X^5-2^5) = 5x^4
----------    ----
f'(x-2)     = 1

如果我们将 x 替换为 2，我们将得到：

5*2^4
----- = 80
1