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Evaluate the limit: lim_{x→0} (sin(5x) − 5x) / x^3. | QuestionStock

$Representative image for question: Evaluate the limit: lim_{x→0} (sin(5x) − 5x) / x^3.$

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Evaluate the limit: lim_{x→0} (sin(5x) − 5x) / x^3.

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Evaluate the limit: lim_{x→0} (sin(5x) − 5x) / x^3.

Options:

−125/6
−125/2
−25/6
0

Correct answer: −125/6

Explanation: Use sin t = t − t^3/6 + O(t^5) with t=5x. The numerator ≈ −(5x)^3/6 = −125 x^3/6, so the limit equals −125/6.

Created 2026-03-10T18:10:01.446Z. Updated 2026-03-10T18:10:01.446Z.