a151q1wi - its Use ∞ and-∞ appropriately to indicate...

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MATH 151 Answers to Assignment 1 Autumn 2009 1. Let f ( x ) = x - sin x x 3 . Find f ( ± 0 . 1), f ( ± 0 . 01), f ( ± 0 . 001) and f ( ± 0 . 0001) correct to five decimal places. Use this to estimate lim x 0 f ( x ). f (0 . 1): 0.16658 f ( - 0 . 1): 0.16658 f (0 . 01): 0.16667 f ( - 0 . 01): 0.16667 f (0 . 001): 0.16667 f ( - 0 . 001): 0.16667 lim x 0 f ( x ): 1 / 6 2. Let f be the function f ( x ) = ( x + 1)( x - 3) ( x - 1)( x + 1) . Find the following limits using limit laws. Give the exact answer using fractions and/or radicals as needed. (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 x y 5 - 5 5 - 5 3. The graph of a certain function f is shown below. Use this graph to find the following lim-
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Unformatted text preview: its. Use ∞ and-∞ appropriately to indicate infnite limits. lim x →-5 + f ( x ): lim x →-2-f ( x ): ∞ lim x →-2 + f ( x ): lim x →-2 f ( x ): DNE lim x →-f ( x ):-4 lim x → + f ( x ):-4 lim x → f ( x ):-4 lim x → 3-f ( x ): 5 lim x → 3 + f ( x ): 4 lim x → 3 f ( x ): DNE lim x → 6-f ( x ):-∞ Typeset using A M S-T E X. MATH 151 Answers to Assignment 1, p . 2 Autumn 2009 end...
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