When x=0 or x→0+, f(x)=0? + 1= 1

When x→0-, f (0-) =1/xsinx+xsin (1/x)

=(sinx)/x+xsin( 1/x)

= 1+0

= 1

Remember: because sin 1/x is a bounded function, when xsin( 1/x) is x→0, xsin( 1/x)=0.

Because f(0+)=f(0-)=f(0)

So x is a continuous point of f(x)

Option d