Question Number 114020 by bemath last updated on 16/Sep/20

lim_(d→∞)  (√(6d)) cos ((2/( (√d)))) sin ((5/( (√d)))) ?

Answered by Olaf last updated on 17/Sep/20

(√(6d))cos((2/( (√d))))sin((5/( (√d)))) ∼_∞  (√(6d))(1−(2/d))((5/( (√d))))  →_(d→∞) 5(√6)

Answered by mathmax by abdo last updated on 16/Sep/20

let f(x) =(√(6x))cos((2/(√x))).sin((5/(√x)))  (d→+∞) ⇒  f(x)∼(√6)(√x)(1−(4/x)).(5/(√x)) =5(√6){1−(4/x)} ⇒lim_(x→+∞) f(x) =5(√6)

Answered by bobhans last updated on 17/Sep/20

letting (1/( (√d) )) = q ∧q→0  lim_(q→0)  ((√6)/q).cos 2q.sin 5q = lim_(q→0)  (√6) cos 2q .lim_(q→0)  ((sin 5q)/q)  = (√6) × 5 = 5(√6)