How can I solve this limit? lim_(x => 1)(sin(x-1))/(x-1)

mundocromadomg 2022-09-14 Answered
How can I solve this limit?
lim x 1 sin ( x 1 ) x 1
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Answers (1)

ruinsraidy4
Answered 2022-09-15 Author has 17 answers
You could simply write down pretty much just what you’ve written here: it shows that you understand why the limit is 1. However, a nice way is to make a substitution y = x 1; then clearly
lim x 1 sin ( x 1 ) x 1 = lim y + 1 1 sin y y = lim y 0 sin y y = 1 .

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