Advertisements
Advertisements
प्रश्न
Evaluate the following :
`lim_(x -> ∞) [(7x^2 + 2x - 3)/(sqrt(x^4 + x + 2))]`
उत्तर
Let L = `lim_(x -> ∞) [(7x^2 + 2x - 3)/(sqrt(x^4 + x + 2))]`
Dividing numerator and denominator by x2, we get,
L = `lim_(x -> ∞) (((7x^2 + 2x - 3)/x^2))/((sqrt(x^4 + x + 2)/x^2))`
= `lim_(x -> ∞) (7 + 2/x - 3/x^2)/sqrt((x^4 + x + 2)/x^4)`
= `lim_(x -> ∞) (7 + 2/x - 3/x^2)/(sqrt(1 + 1/x^3 + 2/x^4)`
= `(lim_(x -> ∞) [7 + 2 xx 1/x - 3 xx 1/x^2])/(lim_(x -> ∞) sqrt(1 + 1 xx 1/x^3 + 2 xx 1/x^4)`
= `(7 + 2 xx 0 + 3 xx 0)/(1 + 1 xx 0 + 2 xx 0) ...[∵ lim_(x -> ∞) 1/x^"n" = 0 "if n" > 0]`
= 7
APPEARS IN
संबंधित प्रश्न
Evaluate the following :
`lim_(x -> ∞) [("a"x^3 + "b"x^2 + "c"x + "d")/("e"x^3 + "f"x^2 + "g"x + "h")]`
Evaluate the following :
`lim_(x -> ∞) [(x^3 + 3x + 2)/((x + 4)(x - 6)(x - 3))]`
Evaluate the following :
`lim_(x -> ∞) [(7x^2 + 5x - 3)/(8x^2 - 2x + 7)]`
Evaluate the following :
`lim_(x -> ∞) [sqrt(x^2 + 4x + 16) - sqrt(x^2 + 16)]`
Evaluate the following :
`lim_(x -> ∞) [sqrt(x^4 + 4x^2) - x^2]`
Evaluate the following :
`lim_(x -> ∞) [((3x^2 + 4)(4x^2 - 6)(5x^2 + 2))/(4x^6 + 2x^4 - 1)]`
Evaluate the following :
`lim_(x -> ∞) [((3x - 4)^3 (4x + 3)^4)/(3x + 2)^7]`
Evaluate the following :
`lim_(x -> ∞) [sqrt(x)(sqrt(x + 1) - sqrt(x))]`
Evaluate the following :
`lim_(x -> ∞) [((2x - 1)^20 (3x - 1)^30)/(2x + 1)^50]`
Evaluate the following :
`lim_(x -> ∞) [(sqrt(x^2 + 5) - sqrt(x^2 - 3))/(sqrt(x^2 + 3) - sqrt(x^2 + 1))]`
Select the correct answer from the given alternatives.
`lim_(x -> ∞) [((2x + 3)^7 (x - 5)^3)/(2x - 5)^10]` =
Evaluate the following :
`lim_(x -> ∞) [((2x + 1)^2*(7x - 3)^3)/(5x + 2)^5]`
Evaluate the following :
`lim_(x -> ∞) [(8x^2 + 5x + 3)/(2x^2 - 7x - 5)]^((4x + 3)/(8x - 1))`
