a151t1au - M ATH 151 Answers to Test 1 Autumn 2009 1. The...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Answers to Test 1 Autumn 2009 1. The graph of a certain function f is below, on the right. Use this graph to Fnd the following limits. Use and -∞ as appropriate. lim x →- 5 + f ( x ): 1 lim x →- 3 - f ( x ): lim x →- 3 + f ( x ): lim x →- 3 f ( x ): lim x 0 - f ( x ): - 1 lim x 0 + f ( x ): - 1 lim x 0 f ( x ): - 1 lim x 2 - f ( x ): 3 lim x 2 + f ( x ): - 1 lim x 2 f ( x ): DNE lim x →∞ f ( x ): - 3 x y 5 - 5 5 - 5 2. ±ind the following limits, where f is the function f ( x )= ( x + 1)( x - 3) ( x - 1)( x + 1) (i) lim x →- 1 f ( x ) = lim x →- 1 x - 3 x - 1 = - 1 - 3 - 1 - 1 Answer : 2 (ii) lim x 2 f ( x ) = lim x 2 x - 3 x - 1 = 2 - 3 2 - 1 Answer : - 1 (iii) lim x 1 + f ( x ): 1 - 3 ± = 0 but 1 - 1 = 0; also for 1 <x< 3 x - 3 x - 1 < 0 because x - 3 < 0 and x - 1 > 0. Answer : -∞ (iv) lim x 1 - f ( x ): 1 - 3 ± = 0 but 1 - 1 = 0; also for x< 1 x - 3 x - 1 > 0 because x - 3 < 0 and x - 1 < 0. Answer : (v) lim x →∞ f ( x ) = lim x →∞ x
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/13/2010 for the course MATH 151 taught by Professor Any during the Winter '08 term at Ohio State.

Page1 / 4

a151t1au - M ATH 151 Answers to Test 1 Autumn 2009 1. The...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online