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# E1Review - Review Exam 1 This is intended to be a tool to...

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Review – Exam 1 * This is intended to be a tool to help you review some of the material that could appear on the exam. It is not inclusive of all topics discussed in lecture. 1. Evaluate the following limits: lim x 2 x 2 + 6 x - 4 x - 2 lim x 3 - x 2 + 3 x - 18 x 2 - 9 lim x →- 3 + x 2 + 3 x - 18 x 2 - 9 lim x 0 + x sin( 1 x ) lim x 2 1 2 - 1 x 2 - 2 2 - x lim x 2 + x 2 + 8 x - 20 | 2 - x | 2. Given that sin( x ) = 8 17 , cos( y ) = 4 5 , x is an angle in Quadrant I, and y is an angle in Quadrant IV, evaluate csc( y ) and tan( x + y ) . 3. Suppose f , g , and h are functions such that lim x →- 1 h ( x ) = 4 , lim x 2 f ( x ) = - 2 , and lim x 2 - g ( x ) = 1 2 . Evaluate lim x →- 1 + h ( fg )( - 2 x ) ( 1 - p h ( x ) ) 2 4. Solve for x in [ - π, π ]: tan( x ) - sin(2 x ) = 0 5. Solve the inequality: 8 - 4 x 2 x 6 6. Find the domain of the following functions: f ( x ) = r x 2 - 8 x g ( x ) = x 2 x 2 - 4 x h ( x ) = x 2 - ln( x ) 7. If f ( x ) = 1 2 + x and g ( x ) = 1 - x 2 , find g ( f ( x ) ) and its domain. 8. Determine r and s so that the piecewise defined function below is continuous on the real line.

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E1Review - Review Exam 1 This is intended to be a tool to...

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