MATA32H3 Lecture 3: 3-Limits-continuity

• School: UTSC
• Department: Mathematics
• Course: MATA32H3
• Professor: Xiamei Jiang

Document Summary

Note f(x) is not defined at x = 1. The limit of f(x) as x approaches a. 1 and f(1) (if it exists) b) lim x . 1 xg and g(1) (if it exists) y = g(x) (1, -1) lim x . 0 xw and w(0) (if it exists) y = w(x) (0, 0) (0, -1) y = f(x) (1, 2) and h(1) (if it exists) d) (1, 3) (1, 1) y = h(x) lim x . 3. 2 properties of limits: constant law, sum law, product law: If f is a polynomial function, thenlim ( : quotient law, root law: n integer. Example 3. 2: find limits: a x lim x. 0. 0000001 2. 71828 x from the right side x. 0. 0000001 2. 7182832 x from the left side x. Limit from the right: if f(x) can be as close as we please to l for all x > a sufficiently close to a (but not equal a).