Is f continuous at x = 0?
A)No
B)Yes

Question

Is f continuous at x = 0? 
A)No 
B)Yes

Quizplus · Accepted Answer

To determine if f is continuous at x=0 we must evaluate the limit of f(x) as x approaches 0 from both the left and right sides, and see if those limits are equal to f(0).

As x approaches 0 from the left side, we have:

f(x) = -x+1 if -1 < x < 0
         = 0 if x = 0

So the limit of f(x) as x approaches 0 from the left is:

lim f(x) = lim(-x+1) = 1
x→0-

As x approaches 0 from the right side, we have:

f(x) = x+1 if 0 < x < 1
         = 0 if x = 0

So the limit of f(x) as x approaches 0 from the right is:

lim f(x) = lim(x+1) = 1
x→0+

Since both the left and right limits equal 1, and f(0) = 0, then the limit of f(x) as x approaches 0 exists and is equal to f(0). Therefore, f is continuous at x = 0. The best choice is B.

Is F Continuous at X = 0