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Review 4 - MAC2233 Chapter 5 Review 1 Evaluate 23/4 43/2 2...

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MAC2233 Chapter 5 Review 1. Evaluate 2 3 / 4 · 4 - 3 / 2 . 2. Simplify the expression x - 3 / 5 x 8 / 3 . 3. Solve the following equation for x : 5 x 2 - 3 = 1 5 2 x . 4. Jada deposited an amount of money in a bank 5 years ago. If the bank had been paying interest at the rate of 5%/year compounded daily (assuming a 365 -day year) and she has $15,000 on deposit today, what was her initial deposit? 5. Determine the accumulated amount if $12,000 is invested for 5 years at an interest rate of 4 %/year with continuous compounding. 6. Write the following expression as the logarithm of a single quantity: ln 2 + 1 2 ln( x + 1) - 2 ln(1 + x ) . 7. Use the laws of logarithms to expand and simplify the expression ln ( e x 1+ e x ) . 8. Use logarithms to solve the following equation for t : A 1+ Be t/ 2 = C. 9. How long will it take an investment of $6000 to grow to $7000 if the investment earns interest at the rate of 6% compounded monthly? 10. Find the derivative of the function f ( x ) = (3 x 2 - 4) e x . 11. Find the derivative of the function g ( t ) = e - 2 t 1+ t 2 . 12. Find the equation of the tangent line to the graph of y = e - x 2 at the point (1 , 1 /e ) . 13. Find the absolute extrema of the function h ( x ) = e x 2 - 4 on [ - 2 , 2]. 14. For the function f ( x ) = e x + e - x 2 find: intervals upon which the func- 1
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tion is increasing and decreasing; intervals upon which the function is concave upward and downward; local max and mins; inflection points; and vertical and horizontal asymptotes. Sketch the curve. 15. Find the derivative of the function f ( x ) = 3 ln x x 2 .
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