lim(h→0)[f(x0+h)-f(x0-h)]/h
=lim(h→0)[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h
=lim(h→0){[f(x0+h)-f(x0)]-[f(x0-h)-f(x0)]}/h
=lim(h→0)[f(x0+h)-f(x0)]/h+lim(h→0)[f(x0-h)-f(x0)]/(-h)
=f`(x0)+f`(x0)
=2f`(x0)
利用导数的定义求下列极限谢谢!
lim(h→0)[f(x0+h)-f(x0-h)]/h
=lim(h→0)[f(x0+h)-f(x0)+f(x0)-f(x0-h)]/h
=lim(h→0){[f(x0+h)-f(x0)]-[f(x0-h)-f(x0)]}/h
=lim(h→0)[f(x0+h)-f(x0)]/h+lim(h→0)[f(x0-h)-f(x0)]/(-h)
=f`(x0)+f`(x0)
=2f`(x0)