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Question
Evaluate the following limits: `lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
Solution
`lim_(y -> 0)[(5y^3 + 8y^2)/(3y^4 - 16y^2)]`
= `lim_(y -> 0) (y^2 (5y + 8))/(y^2 (3y^2 - 16)`
= `lim_(y -> 0) (5y + 8)/(3y^2 - 16) ...[("As" y -> 0"," y ≠ 0),(therefore y^2 ≠ 0)]`
= `(5(0) + 8)/(3(0)^2 - 16`
= `8/(-16)`
= `-1/2`
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