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Practice Exam - Prep101 1. 2. 1 4e 2 x 17e x 4 = 0 2 log x...

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© Prep101 MATH 122 – Practice final 1. Simplify the following algebraic expression 1 2 3 2 3 1 3 2 2 + + + x x x x x 2. solve the following equations 1. 0 4 17 4 2 = + x x e e 2. 3 log ) 2 log( log = + + x x 3. 2 ln(3x+1) + 4 = 5 4. 0 ) (log ) log( 2 4 = x x 5. 5 x+1 – 2 = 4 3. How long will it take money to double if invested at (a) 7% compounded monthly (b) 7% compounded annually (c) 7% simple interest. (d) 7% continuous compound interest 4. Evaluate 3 1 4 lim 3 x x x 5. Evaluate ) 2 ( 2 lim 2 x x x 6. Evaluate x x x x x + + 3 2 7 3 lim 7. Evaluate 1 3 7 2 4 4 lim + + + x x x x x 8. Evaluate 1 3 7 2 4 lim + + + x x x x x 9. Use the definition of derivative to compute f (1) for the function f ( x ) = 5 4 + x . Are there any points on the curve f ( x ) = 5 4 + x where the tangent line is parallel to the line y = x + 1?
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© Prep101 10. Given the function > + = 1 6 1 ) ( 2 2 x x x x a x x f find the value(s) of a for which the function is continuous everywhere. 11. Find the derivative of each of the following functions (a) ) 1 ln( 4 5 + = x e y x (b) ) 1 ln( + = x e x y (c) ) 6 ln( 5 2 x e y x = (d) x e y x ln + = 12. A rectangle is such that one of its vertices is at the origin, one on the positive x
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