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

  • Thread starter Sun God
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  • #1
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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?
 

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  • #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].
 
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  • #3
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Fixed you LaTeX script. There were [ itex] tags mixed in with [ math] tags.
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 [tex]\lim_{n\to\infty} (a_n+ b_n)= A[/itex].
 
  • #4
HallsofIvy
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Thanks, Mark
 

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