Limits at infinity-solutions HW 6

Limits at infinity-solutions HW 6 - handa (nh5757) Limits...

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handa (nh5757) – Limits at infnity – bormashenko – (54880) 1 This print-out should have 15 questions. Multiple-choice questions may continue on the next column or page – fnd all choices beFore answering. 001 10.0 points Determine iF the limit lim x →∞ 3 x +2 x 2 - x +4 exists, and iF it does, fnd its value. 1. limit = 2 2. limit = 0 correct 3. limit = - 3 4. limit = 4 5. limit = 2 4 6. limit doesn’t exist Explanation: Dividing in the numerator and denominator by x 2 ,theh ighestpower,weseethat 3 x x 2 - x = 3 x + 2 x 2 1 - 1 x + 4 x 2 . On the other hand, lim x 1 x =l i m x 1 x 2 =0 . By Properties oF limits, thereFore, the limit exists and limit = 0 . 002 10.0 points Acerta inFunct ion f is known to have the properties lim x →-∞ f ( x )=1 , lim x f ( x )=2 . Determine iF lim x 0+ 2+5 x 3+ f ( 1 x ) exists, and iF it does, compute its value. 1. limit = 7 4 2. limit = 1 3. limit = 1 2 4. limit does not exist 5. limit = 2 5 correct Explanation: The properties oF f ensure that lim x 0 - f ± 1 x ² i m x f ( x , while lim x 0+ f ± 1 x ² i m x f ( x . By properties oF limits, thereFore, lim x 0 - x f ( 1 x ) = 1 2 , while lim x 0+ x f ( 1 x ) = 2 5 . Consequently, lim x 0+ x f ( 1 x ) = 2 5 . 003 10.0 points ±ind all asymptotes oF the graph oF y = 3 x 2 - 10 x +3 3 x 2 - 11 x +6 .
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handa (nh5757) – Limits at infnity – bormashenko – (54880) 2 1. vertical: x = 2 3 , 3 , horizontal: y =1 2. vertical: x = 2 3 , horizontal: y cor- rect 3. vertical: x =3 , horizontal: y 4. vertical: x = 2 3 , 3 , horizontal: y = - 1 5. vertical: x , horizontal: y = - 1 6. vertical: x = 2 3 , horizontal: y = - 1 7. vertical: x = - 2 3 , horizontal: y Explanation: AFter Factorization y = (3 x - 1)( x - 3) (3 x - 2)( x - 3) . Thus y is not defned at x =3,butFor x ± y = 3 x - 1 3 x - 2 ; notice, however, that lim x 3 3 x - 1 3 x - 2 = 8 7 exists, so the graph does not have a vertical asymptote at x =3.S ince ± ± ± 3 x - 1 3 x - 2 ± ± ± -→ ∞ as x 2 3 From the leFt and the right, the line x = 2 3 will, however, be a vertical asymptote. On the other hand, lim x →±∞ 3 x - 1 3 x - 2 , so y =1w i l lbeaho r izon ta laymp to te .
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This note was uploaded on 11/21/2011 for the course M 408N taught by Professor Gualdini during the Spring '10 term at University of Texas at Austin.

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Limits at infinity-solutions HW 6 - handa (nh5757) Limits...

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