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प्रश्न
Evaluate the following :
`lim_(x -> ∞) [((2x + 1)^2*(7x - 3)^3)/(5x + 2)^5]`
उत्तर
`lim_(x -> ∞) [((2x + 1)^2*(7x - 3)^3)/(5x + 2)^5]`
= `lim_(x -> ∞) ((2x + 1)^2/x^2*(7x - 3)^3/x^3)/((5x + 2)^5/x^5)` ...[Divide Numerator and Denominator by x5]
= `(lim_(x -> ∞) ((2x + 1)/x)^2*((7x - 3)/x)^3)/(lim_(x -> ∞)((5x + 2)/x)^5)`
= `(lim_(x -> ∞) (2 + 1/x)^2*lim_(x -> ∞)(7 - 3/x)^3)/(lim_(x -> ∞)(5 + 2/x)^5)`
= `((2 + 0)^2*(7 - 0)^3)/(5 + 0)^5 ...[because lim_(x -> ∞) 1/x^"k" = 0, "k" > 0]`
= `((2)^2 xx (7)^3)/(5)^5`
= `1372/3125`
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