DIRECTIONS. Determine the limit of each function analytically. (Hint: some of the items need to be factored or rationalized for the limits to exist). Answer can be an integer, fraction or decimal - round off to 2 decimal places (hundredths place). 1. lim (3x3 - 5x)" 6. lim Vxz + 12 - 4 x-2 Final Final Answer: Answer: 2. lim (8r - 5x+ 1) X+3 7. lim Va-4 X-16X-16 Final Final Answer: Answer: 3. lim - (x +5)2 8. Jim (m+1)-1 * +5x - 25 Final Final Answer: Answer: 2x- - 5x - 3 4. lim - X-x-12 x ix + 2x -15 9. lim- X-14X--98+20 Final Final Answer: Answer: 4x- x2 5. lim 10. lim (34-2)--(h+2) X-42- VX h-2 h-2 Final Final Answer: Answer:Answer the following problems by showing complete solution. 1. Prepare a probability distribution then find the mean, variance and standard deviation for the courses completed by the students in a certain college. Course Number of Students (X) Tourism 285 HRM 460 Business Administration 152 Mass Communication 185 Architecture and Engineering 98 Total 1,180 2. Results of a study conducted to determine the water consumptions in number of cubic meters of households in a subdivision along with the corresponding probabilities are show below. Find the mean, variance and standard deviation. Number of 48 50 52 54 56 cubic meters (X) Probability P(X) 0.25 0.30 0.18 0.15 0.12 3. The number of inquiries received per day by the Office of Admissions in a certain university is shown below. Find the mean, variance and standard deviation. (15 pts) Number of 22 23 24 25 26 27 Inquiries (X) Probability 0.08 0.19 0.36 0.25 0.07 0.05 P(X) X . P(X X2 . P(X)