Evaluate: `lim_(x->-oo)sqrt(4x^2 + 5x) - 2x`

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The limit `lim_(x->-oo)sqrt(4x^2 + 5x)- 2x` has to be determined.

As x tends to negative infinity 4x^2 tends to positive infinity as the square of a negative number is positive. 5x tends to negative infinity. But the rate at which 4x^2 tends to positive infinity is greater than the rate at which 5x tends to negative infinity. This makes the sum (4x^2+ 5x) tend to positive infinity when x tends to negative infinity.

-2x also tends to positive infinity when x tends to negative infinity.

Adding two terms that tend to positive infinity gives a result of positive infinity.

The required result of the limit is infinity.

`lim_(x->-oo)sqrt(4x^2 + 5x) - 2x = oo`

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