If f(x) = |x|, what is lim_{x→0} f(x)?

If f(x) = |x|, what is lim_{x→0} f(x)?

• A. 0
• B. 1
• C. -1
• D. undefined

Answer: (A)

The limit being tested is about what the function outputs as x gets arbitrarily close to zero. For f(x) = |x|, the value |x| measures distance to zero on the real line. As x approaches zero, that distance shrinks toward zero, so |x| tends to 0. Since absolute value is continuous everywhere, including at zero, the limit exists and equals the value at zero: |0| = 0. The left- and right-hand approaches both approach 0, so the limit is 0. The other options would imply a nonzero limit or no limit, which doesn’t match the behavior of |x| near zero.

The limit being tested is about what the function outputs as x gets arbitrarily close to zero. For f(x) = |x|, the value |x| measures distance to zero on the real line. As x approaches zero, that distance shrinks toward zero, so |x| tends to 0. Since absolute value is continuous everywhere, including at zero, the limit exists and equals the value at zero: |0| = 0. The left- and right-hand approaches both approach 0, so the limit is 0. The other options would imply a nonzero limit or no limit, which doesn’t match the behavior of |x| near zero.