MAT 1300 Lecture 4: MAT 1300 LECTURE 4 –LIMITS and continuity

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 1300
• Professor: Hung-Chang Liao

Document Summary

Take a function say f(x) = x2 we like to compute the slope of a tangent line. Tangent line a line which touches the graph pf f at exactly one point. The slope of pq gets closer to the slope of the tangent as q gets closer to p. F(x) = x if x is not equal to 1. But when x approaches 1 the value f(x) approaches 1. If f(x) approaches the number l when x approaches c from both sides ( but not equal to c ) we write: Lim f(x) =1 { even though f(3) is not defined } x 3. If f(x) l when x c from the right then we write. Lim f(x) = l exists precisely when : Lim f(x) = l = lim f(x) = l. = x+1 when x is not equal to 0. These do not agree therefore the limit does not exist.