Question

if f(x) is continuous at x0 & f(xd) >0 then show that there is an interval i about xd in which f(x)>0

Answer 1

Answer:

Solution:

x→0

lim

f(x)=

x→0

lim

xsin

x

1

=0

at x=0 f(0)=0

x→0

lim

f(x)=f(0)=0

So the givenf(x) is continuous at x=0.