Math 1351 Sample Test 1

Math 1351 Sample Test 11. Solve the equation |2x − 2| = 17.The solutions are x 1 = and x 2 =where x 1 ≤ x 2 .Correct Answers:• -7.5• 9.52. Solve the equation √ 10 − x + x = 8.The only solution is x = .Correct Answers:• 63. Solve the following inequality. Write the answer ininterval notation.|2x − 9| ≤ 12Answer:Correct Answers:• [-1.5,10.5]4. Find the point (0, b) on the y-axis that is equidistantfrom the points (5, 5) and (3, −2).b =Correct Answers:• 25 + (5 − b) 2 = 9 + (2 + b) 2 ) impliesb=37/14 = 2.642857142857145. Find the center and radius of the circle given by theequationx 2 + y 2 + 12x + 8y + 43 = 0The center is : ( , )The radius is :Correct Answers:• -6• -4• 36. A line through (5, −5) with a slope of −4 has ay-intercept atCorrect Answers:• 157. If sin(θ) = 2425, 0 ≤ θ ≤ π/2, thencos(θ) equalstan(θ) equalssec(θ) equalsCorrect Answers:• 7/25 = 0.28• 24/7 = 3.42857142857143• 25/7 = 3.571428571428578. Evaluate the following expressions.sin(cos −1 ( 3 5 ))tan(sin −1 ( 513 ))9. Evaluate the limit10. Evaluate the limit11. Evaluate the limitlimx→3x 3 − 1limx→1 x 2 − 1sin 2x 2limx→0 x 2x − 3x 2 + 5x − 2412. For what value of the constant c is the function fcontinuous on (−∞, ∞) where{y 2 − c if y ∈ (−∞, 5)f(y) =cy + 3 if y ∈ [5, ∞)c =13. If 34900 dollars is invested at an interest rate of7 percent per year, compounded semiannually, find thevalue of the investment after the given number of years.(a) 5 years:Your answer is(b) 10 years:Your answer is(c) 15 years:Your answer is14. Use the Laws of logarithms to rewrite the expressionlog(x 7 y 18 /z 14 )in a form with no logarithm of a product, quotient orpower.After rewriting we havelog(x 7 y 18 /z 14 ) = A log x + B log y + C log zwith the constant1

A =the constantB =and the constantC =15. If ln a = 2, ln b = 3, and ln c = 5, evaluate thefollowing:(a) ln( a−4b 4 c 1 ) =(b) ln √ b 4 c −4 a 4 =(c) ln(a−3 b 3 )ln(bc) −3 =(d) (ln c 1 )(ln ab −3 ) −3 =16. Find the solution of the exponential equatione 2x+1 = 17in terms of logarithms, or correct to four decimal places.x =17. Find the solution of the logarithmic equationlog x + log(x − 11) = log(17x)in terms of logarithms, or correct to four decimal places.Your answer isx =2