The value of the limit \lim_{x\to – \infty } (\sqrt{4x^2 -x} +2x ) is

KVPY SX SB Exam 05-Nov-2017 Question Paper

Question : 3 of 120

Marks: +1, -0

The value of the limit

\lim ↙{x→ – ∞ } (√{4x^2 -x} +2x )

Solution:

Rationalise

\lim ↙{x→ – ∞ } ((√{4x^2 -x} +2x )×{ √{4x^2 -x} -2x }/{√{4x^2 -x} -2x })

\lim ↙{x→ – ∞ }({-x}/{|x|√{4-1/x}-2x})

\at x → –∞ {|x|} = –x

\lim ↙{x→ – ∞ }({-x}/{-x-√{4-1/x}-2x})

=1/{2+2}=1/4

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