106年 - 106 國立暨南國際大學_轉學生入學考試試題_經濟系二：微積分#124192

1. (20%) The US Postal Service (USPS) will accept only packages with length plus girth no more than 108 inches(See the figure). What are the dimensions of the largestvolume package the USPS will accept?

(a)

(b)

3. (20%) I want to fence in a rectangular vegetable patch. The fencing for the east and west sides costs $5 per foot, while the fencing for the north and south sidescosts only $3 per foot. I have a budget of $150 for the project. What is the largestarea I can enclose?.

(a) f(x) = (x⁹ + 8)lnx

(b) f(x) = ln

(a) (8%) Please sketch the graph of the pulse function.

(b) (12%) Find the following limits:
(i) lim_x→0P_a,b(x) (ii) lim_x→a⁺P_a,b(x) (iii) lim_x→a^-P_a,b(x)