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lim x→0 √(x²+4)-2/x²​

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Abidemiokinidn

The limit of the given function is 1/2

Limit of a function

Given the following limit of a function

lim x→0 √(x²+4)-2/x²​

Substitute the limit to have:

√(0²+4)-2/0²​

√4 - 2/0

2-2/0

0/0 (ind)

Apply the L'hospital rule to have;

lim x→0 d/dx√(x²+4)-2/(d/dx)x²​

lim x→0 (x²+4)^-1/2 * 2x/2x

lim x→0 (x²+4x)^-1/2

Substitute

(4)^-1/2

1/2

Hence the limit of the given function is 1/2

Learn more on limit of a function here; https://brainly.com/question/23935467

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