用洛必达法则
lim(x→2)F(x)
=lim(x→2) [x^2∫[2,x]f(t)dt]/(x^2-4) (0/0)
=lim(x→2) [2x∫[2,x]f(x)dx+x^2f(x)]/(2x)
=lim(x→2) [2∫[2,x]f(x)dx+xf(x)]/x
=2f(2)
用洛必达法则
lim(x→2)F(x)
=lim(x→2) [x^2∫[2,x]f(t)dt]/(x^2-4) (0/0)
=lim(x→2) [2x∫[2,x]f(x)dx+x^2f(x)]/(2x)
=lim(x→2) [2∫[2,x]f(x)dx+xf(x)]/x
=2f(2)