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Finding the limit of the sum of two terms that individually have different limits

  1. May 14, 2010 #1
    For instance:

    1/(e^.5t) + 1/(e^-7t)

    As t grows larger, the left term goes to 0, but the right term goes to infinity.

    Would I be correct in saying that the limit of the sum is infinity because the (absolute value of the) coefficient of t in the term that tends to infinity is larger than the coefficient of t in the term that tends to 0?

    What if both t's had the same coefficient?
     
  2. jcsd
  3. May 14, 2010 #2

    HallsofIvy

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    It doesn't matter what the coefficients are. If [itex]\{a_n\}[/itex] and [itex]\{b_n\}[/itex] are any two sequences such that [itex]\lim_{n\to\infty} a_n= \infty[/itex] and [itex]\lim_{n\to\infty}b_n= 0[/itex], then [itex]\lim_{n\to\infty} (a_n+ b_n)= \infty[/itex].

    More generally, if [itex]\lim_{n\to\infty} a_n= A[/itex] and [itex]\lim_{n\to\infty}b_n= 0[/itex], then [itex]\lim_{n\to\infty} (a_n+ b_n)= A[/itex].
     
    Last edited: May 15, 2010
  4. May 14, 2010 #3

    Mark44

    Staff: Mentor

    Fixed you LaTeX script. There were [ itex] tags mixed in with [ math] tags.
     
  5. May 15, 2010 #4

    HallsofIvy

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    Thanks, Mark
     
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