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