Find lim (x - 0) (7x - sin(x)) / (x^2 + sin(3x)). Choose 1 answer: A) 2 B) 1 C) 0 D) The limit doesn't exist.

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Find lim (x -> 0) (7x - sin(x)) / (x^2 + sin(3x)). Choose 1 answer: A) 2 B) 1 C) 0 D) The limit doesn't exist.

SnapAndSolve AI · Accepted Answer

To find the limit, we use L'Hôpital's Rule, which applies when the limit is in the indeterminate form 0/0. Differentiate the numerator and the denominator:

Numerator: d/dx (7x - sin(x)) = 7 - cos(x)
Denominator: d/dx (x^2 + sin(3x)) = 2x + 3cos(3x)

Now, evaluate the limit:

lim (x -> 0) (7 - cos(x)) / (2x + 3cos(3x))

Substitute x = 0:

(7 - cos(0)) / (2(0) + 3cos(0)) = (7 - 1) / (0 + 3) = 6 / 3 = 2

The answer is A) 2.

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Find lim (x -> 0) (7x - sin(x)) / (x^2 + sin(3x)). Choose 1 answer: A) 2 B) 1 C) 0 D) The limit doesn't exist.

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