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lim x → ∞ (x(sin (7/x)))?
webassign says "Hint: Let x = 1/t and find the limit as t → 0+" but i keep getting 0 as the limit anyway and that's not the right answer.......
please explain how to solve this in detail :)
3 Answers
- Anonymous4 years ago
limit x->infinity [x*sin(7/x)]
t = limit x->infinity 7/x = 7 * limit x->infinity 1/x = 7 * 0 = 0 ; x = 7/t
limit t->0 (7*sin(t)/t) = 7
- ?Lv 74 years ago
When x is extremely large, then 7/x is a small number. Sin 7/x=7/x. You get the limit as x 7/x=7
- ?Lv 74 years ago
note lim t → 0 sin(t)/t = 1
lim x→∞ x*sin(7/x)
= lim x→∞ 7/(7/x) sin(7/x)
let t = 7/x
= lim t→0 7*sin(t)/t
= 7 lim t→0 sin(t)/t
= 7*1 = 7
