tutorial 3sol

tutorial 3sol - MATH 1007- TUTORIAL 3 1. Find the following...

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MATH 1007- TUTORIAL 3 1. Find the following limits, if they exist. i) lim lim () lim x xx x x x x x x −+ = = + = + = 1 2 21 2 1 1 1 2 11 1 1 1 0 ii) lim lim lim x x x x x x x →− = = + 1 2 2 1 1 1 2 1 1 1 DNE since lim x x x + =−∞ + 1 1 1 and lim x x x + =∞ 1 1 1 . iii) lim x x 1 2 2 1 = == lim x x 1 2 2 1 00 iv) lim lim lim x x x x x x x x x x x x x −+ − = +− = 3 3 3 2 3 3 3 3 3 2 3 3 333 2 3 3 = = =− lim lim ( ) lim x x x x x x 3 2 33 3 3 133 3 3 13 3 1 9 .( ) . v) lim lim . lim lim t t t t t t t t t t tt t t = +− ++ ++ = = = 0 0 0 0 1 1 2 vi) lim lim lim . x x x x x x x x x + ⎟ = + = + 0 1 9 1 3 1 0 39 0 = + = + = + lim lim ) x x x x 0 99 39 3 9 0 1 3 9 1 33 3 3 1 54 2. Let fx xf o r x o r x o r x , , , = +< −≤ > 1 2 0 0 1 2 1 a) Find: i) lim ( ) lim ( ) x x x = += −− 1 2 1 ii) lim ( ) lim x x x = −= 1 iii) lim ( ) lim x x x = 1 iv) lim ( ) lim x x x = = 2 b) Is f continuous at x = 0 ? Why or why not?
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This note was uploaded on 03/22/2010 for the course MATH 1007 taught by Professor Unknown during the Fall '07 term at Carleton.

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tutorial 3sol - MATH 1007- TUTORIAL 3 1. Find the following...

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