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Limits

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School
University of Toronto St. George
Department
Mathematics
Course
MAT135H1
Professor
all
Semester
Summer

Description
LIMITS     Knowledge  Summary       The  limit  of  a  function  f  (x)  is  the  value  that  the  function  approaches  as  x  approaches  a  specific   value,  a,  or  infinity.    If  the  limit  of  a  function  seems  at  first  to  approach  0/0,  the  limit  might  need  to   be  rearranged  by  some  of  the  limit  rules  to  be  evaluated.     Basic  limit  rules:   lim 𝑥 = 𝑎   ▯→▯ 1 ▯→▯m = 0   𝑥 lim 1 = ∞        (𝑇𝐻𝐸  𝐿𝐼𝑀𝐼𝑇  𝐷𝑂𝐸𝑆  𝑁𝑂𝑇  𝐸𝑋𝐼𝑆𝑇)   ▯→▯ 𝑥   Ratio/product  rule:   𝑓 𝑥 lim𝑓 𝑥 lim = ▯→▯   ▯→▯ 𝑔 𝑥 lim𝑔 𝑥 ▯→▯ lim 𝑓 𝑥 ∗ 𝑔 𝑥 = lim𝑓 𝑥 ∗ lim𝑔 𝑥   ▯→▯ ▯→▯ ▯→▯   Sum  rule:   ▯→▯ 𝑓 𝑥 + 𝑔 𝑥 = l▯→▯ 𝑥 + lim𝑔 𝑥 ▯→▯   Constant  rule:   lim 𝑐 ∗ 𝑓 𝑥 = 𝑐 ∗ lim𝑓 𝑥   ▯→▯ ▯→▯   Combination  rule:   lim𝑓 𝑔 𝑥 = 𝑓 lim𝑔 𝑥   ▯→▯ ▯→▯   Examples:                                   (from  midterm  2004,  question  3)                                                       (from  midterm  2002,  question  5)                                               (from  midterm  2008,  question  6)                                                                   (from  midterm  2009,  question  9)                                       Past  Questions:
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