Josh D.

asked • 03/11/24

Calculus Help!!!

Evaluate lim x→0 (2sin(x)−sin(2x))/(2e^x −2−2x−x^2)


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Valentin K. answered • 03/11/24

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This is type 0/0. Use L'Hospital, twice.

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Josh D.

shouldn't it be 3?
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03/12/24

Valentin K.

tutor
Yes 3 times.
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03/12/24

Josh D.

thank you so much! cause like i got 6/2 and then I got 3 (by using the l hospital rule).
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03/12/24

Valentin K.

tutor
Keep in mind that you can use L'Hospital only when the limit is of certain type, in this case 0/0, and you can keep using it repeatedly while the limit matches one of the allowed types. In this case the idea of using it several times was that all intermediate limits were of type 0/0 and every use of L'Hospital decreased the powers of x in the denominator.
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03/12/24

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