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
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