Evalute limits involving the by constructjng their respective table of values
1.lim t -> 0 t/(sin t)
2.lim t -> 0 (sin t)/(2t)•(1 - cot t)/t
3.lim t -> 0 (e ^ t - 1/t)
1
Expert's answer
2022-03-31T08:51:52-0400
limt→0sintt=limt→0(tsint)−1=1. It contains the well-known limit tsint The values of function sintt near are: t=0.05,sintt≈1.0004;t=0.03,sintt≈1.0002;t=0.01;sintt≈1.00002. From the latter we can conclude that the limit is 1. Another way to compute the limit is to use L'Hôpital's rule.
limt→02tsintt1−cott=+∞ . The first fraction is the well-known limit multiplied by 21. The second fraction can be rewritten in the form: t1−cott=t1−sintcost=tsintcost−sint. This fraction approaches infinity (the term cost−sint approaches 1 and the term tsint approaches 0). Another way to compute the limit is to use L'Hôpital's rule.
limt→0tet−1=1. It is the well-known known limit tet−1 . The values of function tet−1 near are: t=0.05, tet−1≈1.0152;t=0.03,tet−1≈1.0152;t=0.01,tet−1≈1.0050. Another way to compute the limit is to use L'Hôpital's rule.
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