Find \(\displaystyle\lim_{{{n}\to\infty}}{\frac{{{n}+{\sin{{\left({n}^{{{2}}}\right)}}}}}{{{n}+{\cos{{\left({n}\right)}}}}}}\)

zdebe5l8

zdebe5l8

Answered question

2022-04-14

Find limnn+sin(n2)n+cos(n)

Answer & Explanation

cutimnm135imsa

cutimnm135imsa

Beginner2022-04-15Added 21 answers

limnn+sin2(n)n+cos(n)1=limnsin2(n)cos(n)n+cos(n)=0,
since the numerator is bounded and the denominator tends to +. Therefore
limnn+sin2(n)n+cos(n)=1
shanna87mn

shanna87mn

Beginner2022-04-16Added 19 answers

Observes that
n+sin(n2)n+cos(n)=1+sin(n2)n1+cos(n)n1
Since
sin(n2)n0  and  cos(n)n0

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