Question

The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______ 

विकल्प

• `-1/sqrt5`

• 0

• `1/sqrt5`

• 1

Answer 1

The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is `underline(-1/sqrt5)`.

Explanation:

Put x = -y

As x → -∞, y → ∞

∴`lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4) = lim_{y→ ∞}sqrt(5(-y)^2 - 4y + 7)/(-5y + 4)`

= `lim_{y→ ∞} sqrt(5 - 4/y + 7/y^2)/(-5 + 4/y)`

= `sqrt5/-5`

= `-1/sqrt5`