{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

a151t1au

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

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

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

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### 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
Ask a homework question - tutors are online