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Question
The value of `lim_{x→-∞} (sqrt(5x^2 + 4x + 7))/(5x + 4)` is ______
Options
`-1/sqrt5`
0
`1/sqrt5`
1
MCQ
Fill in the Blanks
Solution
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`
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Limits of Exponential and Logarithmic Functions
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