用跟ichban很像又不太像的做法
令\(\displaystyle f(x)=\int_a^x \frac{1}{1+x^4}dx\)
\(\displaystyle \lim_{h \to 0}\frac{1}{h}\int_{(3+h)^2}^9\frac{1}{1+x^4}dx\)
\(\displaystyle =\lim_{h\to 0}\frac{f(9)-f(h(h+6)+9)}{h}\)
\(\displaystyle =\lim_{h\to 0}(h+6)\times \frac{f(9)-f(h(h+6)+9)}{h(h+6)}\)(乘法的左右極限值皆存在)
\(\displaystyle =\lim_{h\to 0}(h+6)\times \lim_{h(h+6)\to 0}\frac{f(9)-f(h(h+6)+9)}{h(h+6)}\)
\(\displaystyle =6\times(-f'(9))\)
\(\displaystyle =\frac{-6}{1+9^4}\)
