Practice Exam - © Prep101 MATH 122 – Practice final 1 Simplify the following algebraic expression 3x 1 3x 2 −2 x − 3x 2 x − 1 2 2 solve

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Unformatted text preview: © Prep101 MATH 122 – Practice final 1. Simplify the following algebraic expression 3x + 1 3x + 2 −2 x − 3x + 2 x − 1 2 2. solve the following equations 1. 4e 2 x − 17e x + 4 = 0 2. log x + log( x + 2) = log 3 3. 2 ln(3x+1) + 4 = 5 4 2 4. log( x ) − (log x) = 0 5. 5x+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 lim x →3 5. Evaluate 4 − x −1 x−3 x−2 lim ( x − 2) x→2− x 2 − 3x + 7 Evaluate lim x3 + x x →∞ 6. 7. Evaluate 2x 4 + x + 7 lim − 3x 4 + x − 1 x →∞ x4 + x + 7 8. Evaluate lim 2 x →∞ − 3 x + x − 1 9. Use the definition of derivative to compute f’(1) for the function f(x) = 4 x + 5 . Are there any points on the curve f(x) = 4 x + 5 where the tangent line is parallel to the line y = x + 1? © Prep101 ⎧x 2 − a 2 x f ( x) = ⎨ ⎩ x+6 10. Given the function x ≤ −1 x > −1 find the value(s) of a for which the function is continuous everywhere. 11. Find the derivative of each of the following functions 5x 4 (a) y = e ln( x + 1) x (b) y = x ln(e + 1) 2 5e x (c) y = ln(6 x) (d) y = e x + ln x 12. A rectangle is such that one of its vertices is at the origin, one on the positive x‐axis, one on the 2 positive y‐axis and the last one on the curve y = 1 − x . Find the maximum area of this rectangle. 13. Write an equation for the tangent line at the point P(1 ,1) on the curve 2( x + y ) − 2 x + y = 15 3 2 2 3 14. A point is traveling on the curve y + x = 5 . When the x‐coordinate is 1 it is decreasing at the rate 2 cm/s. Find the rate at which the y‐coordinate is changing given that y is positive. 15. Evaluate the following integrals ⎛ • ∫⎜e ⎝ • ⎜ ∫⎜ ⎝ ⎛ 1⎞ + x 2 + ⎟dx x⎠ 2⎞ x + 3 ⎟dx ⎟ x⎠ x 16. Evaluate the following integrals • ∫e • e ∫ x (e x − 2) 4 dx x x dx ∫ x e dx 2x 17. Evaluate the following integral ...
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This note was uploaded on 02/11/2010 for the course MANAGEMENT MATH 122 taught by Professor Sidneytrudeau during the Winter '10 term at McGill.

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