MAT 295 Lecture 3: Calculating Limits

• School: Syracuse University
• Department: Mathematics
• Course: MAT 295
• Professor: All

Document Summary

Assume f(x) is defined on an open interval containing the number a , except possibly at. Definition: lim x a f (x )=l if for every (arbitrarily small) number 0 there is a (sufficiently small) number 0 such that if x a , then. This means that by choosing x a sufficiently small, we can make. F (x) l smaller than any given 0 . Dsp also holds if f(x) is a rational function and a is in the domain of f(x) f (x)=f (a) Example: evaluate (3 x4+5 x2) lim x 2. For this problem, the direct substitution property doesn"t work for this limit problem, soh we need to factor out the function first lim x 2 x2 5x+6 x2 4 (x 3)(x 2) lim x 2 (x 2)(x+2) The (x-2) cancel out and now we can continue using the dsp (x 3) lim x 2 (x+2) lim x 0.