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MATH 142 Business Math II, Week In Review Spring, 2015, Problem Set 3 (Exam1 Review) JoungDong Kim 5x4 − 3x2 + 2x + 3 . x→0 9x2 − 4 1. Evaluate lim x2 + x − 20 2. Find lim 2 x→4 x − 7x + 12 1 3. For what values of x is f (x) continuous x2 − 4 x−2 f (x) = 10x + 20 x+6 4. Evaluate f ′ (x) if f (x) = √ x+3 2 if x ≤ 4 if x > 4 5. Consider the graph of f (x) below, what are f ′ (−4), f ′ (−2), f ′ (1), and f ′ (4). y 5 4 3 2 1 x −5 −4 −3 −2 −1 6. If f (3) = 7 and f ′ (x) = √ 3 1 2 3 4 5 2x2 − 10 for all x, find the tangent line to f (x) at x = 3. 3 7. Given logb 5 = −2.3219 and logb 7 = −2.8074, what is the value of logb 8. Solve for x: log7 (3 − x) + log7 (−x) = log7 54 9. Find the domain of the function: f (x) = √ 3 x2 4 x−3 − 7x + 12 35 . b3 10. Cathy wants to have $19,000 in cash 6 years from now in order to pay for improvements that must be made to her small office at that time. If Cathy finds a saving account that pays annual interest of 4.2% compounded monthly, then how much should she invest right now in the account in order to have the funds in 6 years? (Round your answer to the nearest cent) 11. Find the effective yield given an annual rate of 12% compounded monthly. 12. What transforms of y = f (x) will yield y = −3f (x + 1) + 7. 5 13. Susan and Sharon own a flower shop. Their monthly price-demand equation is given by p = −4x + 136, where x is the number of arrangements sold and p is given in dollars. The girls have determined that they have fixed costs of $900, and that it costs them $15 to make each arrangement. What price (in dollars) should they charge to maximize their revenue? What is the average rate of change of profit (in dollar/arrangement) where production goes from 8 to 15 arrangements each month? 6 14. Solve for x (4x+2 )(162x−5 ) + 6 = 10 15. How long will it take a $600 investment to be worth $1100 if it is continously compounded at 12% per year? (Give your answer to three decimal places) 7 16. Graph the given function: f (x) = x2 + 3 2x − 1 if x < 2 if x ≥ 2 17. A golf club manufacturer has monthly fixed cost of $990. It costs $25 to manufacture each golf club, and each golf club sells for $70. How many golf clubs must be produced in order for the manufacturer to break even? (If needed, round your final answer to the nearest integer) 18. Determine the domain of the following function x−2 (2x + 4)(x − 2) f (x) = 8 3−x e x+7 8 if x < 3 if x = 3 if x > 3