SOLUTION: Evaluate limit (as x approaches negative infinity) (10x-3)/(sqrt(5x^2-x^3-7x+1))

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Question 1200138: Evaluate limit (as x approaches negative infinity) (10x-3)/(sqrt(5x^2-x^3-7x+1))
Answer by ikleyn(52898) About Me  (Show Source):
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Evaluate limit (as x approaches negative infinity) (10x-3)/(sqrt(5x^2-x^3-7x+1))
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As x approaches negative infinity, the numerator behaves as  -10*|x|,


while the denominator behaves as  -sqrt%28abs%28x%5E3%29%29 = -abs%28x%29%5E1.5.




So the rational function behaves as  %2810%2Aabs%28x%29%29%2Fabs%28x%29%5E1.5 = 10%2Fabs%28x%29%5E0.5,


i.e. tends to zero, as x approaches minus infinity.


ANSWER.  The limit is 0 (zero).

Solved.


Vertical lines in my post denote absolute value (a standard designation).