The value of the limit `lim_(x to -oo) (sqrt(4x^(2) - x )+2x)` is
The value of the limit `lim_(x to -oo) (sqrt(4x^(2) - x )+2x)` is
A. `-oo`
B. `-(1)/(4)`
C. 0
D. `(1)/(4)`
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Correct Answer - D
Rationalise
` lim_(x to -oo) ((sqrt(4x^(2) - x) + 2x) xx (sqrt(4x^(2) - x) - 2x)/(sqrt(4x^(2) -x)- 2x))`
`lim_(x to -oo) ((-x)/(|x|sqrt(4 - (1)/(x)) - 2x)) "at" x to -oo |x| = - x `
`lim_(x to -oo) ((-x)/(|x|sqrt(4 - (1)/(x)) - 2x)) = (1)/(2+ 2) = (1)/(4)`
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