Question

show that the function f( x)=2x-|x| is continuous at x=0.

Answer 1

for function to be continous at a point
it's left hand limit =rhl
f(0+h)=f(0-h)
f(h) should be equal to f(-h)
f(h)=2h-|h|=h=0(limit h tends to zero)
f(-h) =2(-h) -h=-3h=0(limit h tends to 0)
since both are equal.. hence function is continus at x=0