Evaluate `lim_(x rarr oo) (3x^(2)+4x+5)/(4x^(2)+7)`.

1.	Evaluate `lim_(x rarr oo) (3x^(2)+4x+5)/(4x^(2)+7)`.
Answer» Put `x = (1)/(y), "when" x rarr oo, y rarr 0` `therefore underset(x rarr oo)("lim")(3x^(2)+4x+5)/(4x^(2)+7)=underset(y rarr 0)("lim")(3(1)/(y^(2))+4(1)/(y)+5)/(4*(1)/(y^(2))+7)` `" "=underset(y rarr 0)("lim")(3+4y+5y^(2))/(4+7y^(2))=(3+0+0)/(4+7(0))=(3)/(4)`.

Discussion

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