LIMIT AND CONTINUITY

Solutions: 1. When x is close to a and x ≠ a , f(x) is close to l

2. lim_{x→a} f(x) exists , and lim_{x→a} f(x) = f(a)

3. (1) 3 (2) \frac{1}{2} (3) does not exists

4. (i) (1)2 (2) 2 (3) does not exists (ii) g is not continuous at 0. (^{·}_{·}^{·} lim_{x→0} g(x) does not exist.)

5. (i) (1) 2 (2) 2 (3) 2 (ii) h is continuous at 2. (^{·}_{·}^{·} lim_{x→−1} h(x) = h(−1))