Find lim x→0 x cos(x) / ((x + 1) sin(x)).
Choose 1 answer:
A) 1/2
B) 1
C) 0
D) The limit doesn't exist.

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Find lim x→0 x cos(x) / ((x + 1) sin(x)). Choose 1 answer: A) 1/2 B) 1 C) 0 D) The limit doesn't exist.

SnapAndSolve AI · Accepted Answer

Answer: A) 1/2Explanation: As x approaches 0, both the numerator and the denominator approach 0, so we can apply L'Hôpital's Rule. Differentiate the numerator and the denominator: Numerator: d/dx [x cos(x)] = cos(x) - x sin(x) Denominator: d/dx [(x + 1) sin(x)] = sin(x) + (x + 1) cos(x) Evaluate the limit again:lim x→0 [cos(x) - x sin(x)] / [sin(x) + (x + 1) cos(x)] = cos(0) / (sin(0) + cos(0)) = 1 / 2.

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Find lim x→0 x cos(x) / ((x + 1) sin(x)). Choose 1 answer: A) 1/2 B) 1 C) 0 D) The limit doesn't exist.

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