plugin-thq1

# plugin-thq1 - Differential Calculus Fall 2010 Take-Home...

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Differential Calculus Fall 2010 Take-Home Quiz 1 1. Find the domain and range of the function 1) y = x 2 + 1 2) y = - x - 2 3) y = 1 x + 2 2. Evaluate the function as indicated. Determine its domain and range. f ( x ) = ( 3 x + 3 , x < 1 - x 2 - 3 , x 1 f ( - 2) , f (3) , f ( t 2 + 5) Find the composite functions ( f g ) and ( g f ). What is the domain of each composite function? 3. f ( x ) = x 2 + 1 , g ( x ) = sin x 4. f ( x ) = x 2 + 3 , g ( x ) = 1 x - 2 5. Find the limit L . Then use the ε - δ definition to prove that the limit is L . lim x 2 (2 x - 3) 6. Find the limit. 1) lim x 2 (2 x 3 - x + 5) 2) lim x 2 x + 4 x 2 + 1 3) lim x →- 2 cos πx 7. Use the information to evaluate the limits lim x c f ( x ) = - 3 , lim x c g ( x ) = 5 1) lim x c 2 f ( x ) + q g ( x )

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2) lim x c 3 f ( x ) q g ( x ) Find the limit (if it exists). 8. lim x →- 1 x 2 - x - 2 x 2 - 1 9. lim x 3 x 2 - 9 x 2 - 5 x + 6 10. Find the limit (if it exists). lim x 1 x + 3 - 2 x 2 - 1 Determine the limit of the trigonometric function (if it exists)
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