Boxed limit

Calculus Level 2

Find the limit to 3 places of decimal

lim ⁡ x → ∞ x 5 ⌊ 1 x 3 ⌋ \large \lim_{x \rightarrow \infty} x^{5} \left\lfloor \dfrac{1}{x^3} \right\rfloor


The answer is 0.000.

Md Zuhair by Md Zuhair , 20, India

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1 solution

Jerry McKenzie
Dec 28, 2017

We see that the floor function of ⌊ 1 x 3 ⌋ = 0 ∀ x ∈ ( 1 , ∞ ) \lfloor\frac{1}{x^{3}}\rfloor = 0\enspace\forall x\in(1,\infty ) , since the floor function (brackets) makes us round down.

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