Continuity and One-Sided Limits

Question 1

The limit of f(x) as x → c exists if and only if:

• Af(c) is defined
• Bthe left-hand and right-hand limits both exist and are equal
• Cthe right-hand limit exists
• Df is a polynomial

Question 2

Which of the following is NOT one of the three conditions for continuity at x = c?

• Af(c) is defined
• Blim f(x) exists as x → c
• Clim f(x) = f(c)
• Df is differentiable at c

Question 3

The notation lim f(x) as x → c⁻ denotes:

• Athe left-hand limit
• Bthe right-hand limit
• Cthe two-sided limit
• Dthe value f(c)

Question 4

If any one of the three conditions for continuity fails at x = c, then f is:

• Acontinuous at c
• Bdifferentiable at c
• Cdiscontinuous at c
• Dconstant near c

Question 5

For f(x) = 2x² + x − 5, the left-hand and right-hand limits at x = 1 are:

• Aboth 2
• Bboth −2
• C−2 and 2
• Dboth 0