Let α , β ∈ R be such that lim x → 0 ⁡ x 2 sin ⁡ β x α x - sin ⁡ x = 1 . Then 6 α + β equals

Question

Let &#945; , &#946; &#8712; R be such that lim x &#8594; 0 &#8289; x 2 sin &#8289; &#946; x &#945; x - sin &#8289; x = 1 . Then 6 &#945; + &#946; equals

Quantrex Academy · Accepted Answer

Correct answer: 7

If &#945; &#8800; 1 , then lim x &#8594; 0 x sin &#946; x &#945; x - sin x x = 0 &#8756; &#945; = 1 &#8658; lim x &#8594; 0 &#946; x 3 sin &#946; x &#946; x x 3 x - sin x x 3 = &#946; 1 6 Using, lim x &#8594; 0 x - sinx x 3 = 1 6 &#160;&#38; lim x &#8594; 0 sinx x = 1 &#8658; 6 &#946; = 1 &#8658; &#946; = 1 6 &#8658; 6 &#945; + &#946; = 7

Let α , β ∈ R be such that lim x → 0 ⁡ x 2 sin ⁡ β x α x - sin ⁡ x = 1 . Then 6 α + β equals

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Step-by-step solution

More from Limits

Let &#945; , &#946; &#8712; R be such that lim x &#8594; 0 &#8289; x 2 sin &#8289; &#946; x &#945; x - sin &#8289; x = 1 . Then 6 &#945; + &#946; equals

Correct answer

Step-by-step solution

More from Limits

Let α , β ∈ R be such that lim x → 0 ⁡ x 2 sin ⁡ β x α x - sin ⁡ x = 1 . Then 6 α + β equals