Show that #|c|<1# ?
Given #f# continuous , #f:RR->RR#
If #f(x)!=0# for #x# #in# #(-oo,c)uu(c,+oo)# and
#f(1)f(-1)<0#
then show that #|c|<1#
Given
If
then show that
1 Answer
Jan 18, 2018
Solved.
#f(1)f(-1)<0#
According to Bolzano Theorem (generalization)
Supposed
- If
#c>=1# then#f(x)!=0# if#x# #in# #(-oo,c)uu(c,+oo)#
However,
CONTRADICTION!
- If
#c<=-1# then#f(x)!=0# if#x# #in# #(-oo,c)uu(c,+oo)#
However,
CONTRADICTION!
Therefore,