MATH 140 Lecture Notes - Lecture 3: Quotient Rule, Product Rule
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Math 140 lecture 3 limits (continued) To find > 0 so that if 0 < |x-3| < , then |f(x)-7| < , then |2x-4| < , then |x-3| < /2: ex 2, let g (x)={ 2x ,x <1. Show that lim x 1 g( x)=2 : we will need to look at both cases individually, case 1: let > 0. Find > 0 so that if 0 < |x-1| < and x < 1, then |2x-2| < , then. |x-1| < /2: case 2: to find 2 > 0 so that if 0 < |x-1| < 2, then |(4x-2)-x| < and x > 1, then | 4x 4| < , then |x 1| < /4: finally, let be the minimum of the two values, which is /4. =lim x a: quotient rule - lim x a lim x a, ex: (x3 3x+2) lim x 2 (4x+1) lim x 2 lim x 2 x3+lim x 2 lim.