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Test 2 sols

# Test 2 sols - TEST 2 SOLUTIONS 1.15pts Find the limits USE...

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1 TEST 2 SOLUTIONS 1.15pts Find the limits: USE THE TECHNIQUES NOT TABLES. If the answer is ±∞ do not write “does not exist”: a) ( ( ( 29( 29 ( ( ( 29( 29 2 2 1 1 1 1 1 5 1 5 6 5 5 lim lim lim lim 4/5 3 4 1 4 1 4 4 x x x x x x x x x x x x x x x x x x →- →- →- →- + + + + + + + = = = = - - - + - + - - b) 2 2 lim 4 x x x + = +∞ - [Since x > 2, the bottom is very small and + and the top is near 2, so we have division by a very small pos #] c) ( 29 ( ( 29 ( 29 ( 29 ( 9 9 9 9 3 9 3 9 lim lim lim 6 9 3 3 3 x x x x x x x x x x x x - + - + - = = = - - - + 2.15pts Find the limits. If the answer is ±∞ do not write “does not exist”: a) 2 2 2 2 5 4 5 lim lim 5/ 2 2 3 2 x x x x x x x →-∞ →-∞ - = = b) 1 1 0 lim 1 1 1 0 x x x e e →- ∞ - - = = - c) ( ( 2 2 2 2 2 2 3 3 3 lim lim 0 3 3 x x x x x x x x x x x x →+∞ →+∞ + - + + + - = = + + + + 3.5pts Given that : ( ( lim 3 , lim 5 x x f x g x →+ ∞ →+ ∞ = = - find the following: ( ( ( ( lim 3 3 3 5 12 x f x g x →+ ∞ = + - = 4.6pts Is the function ( 29 4 10 , 4 6 , 4 x x g x x - = - = continuous at x = 4? Why or why not?

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