find limit as x approaches 3 of the quotient of the quantity the square root of the quantity 2 times x plus 3 minus the square root of 3 times x and the quantity x squared minus 3 times x . you must show your work or explain your work in words. (10 points)

Atextile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. the company wishes to test the hypothesis upper h subscript 0 baseline colon mu equals 12 against upper h subscript 1 baseline colon mu less-than 12 using a random sample of n equals 4 specimens. calculate the p-value if the observed statistic is x overbar equals 11.8. round your final answer to five decimal places (e.g. 98.76543).