高数,求极限请问若f'(x0)=1,则limh→0=[f(x0+2h)-f(x0)]/h=?若f'(x0)=1,则limh→1=[f(x0+2h)-f(x0)]/h=?

Question

高数,求极限
请问
若f'(x0)=1,则lim h→0 = [ f(x0+2h)-f(x0) ] / h=?
若f'(x0)=1,则lim h→1 = [ f(x0+2h)-f(x0) ] / h=?

Answer 1

若f'(x0)=1,则lim h→0 = [ f(x0+2h)-f(x0) ] / h
=lim h→0 = [ f(x0+2h)-f(x0) ] / 2h ×2
=2f'(x0)
=2
若f'(x0)=1,则lim h→1 = [ f(x0+2h)-f(x0) ] / h
=[ f(x0+2)-f(x0) ] /1
=f(x0+2)-f(x0)