A ski rental shop charges $6.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $48.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.
A) $15.00
B) $12.00
C) $18.00
D) The limit does not exist.

Question

A ski rental shop charges $6.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $48.00 for all day. If  equals the total charge for the ski equipment for t hours, determine the limit  , if it exists.
A) $15.00 
B) $12.00 
C) $18.00 
D) The limit does not exist.

Quizplus · Accepted Answer

The total charge, 11eaa948_cdc9_6a48_84bc_9751c5186ed9_TB2342_11, is given by:
- If t is less than or equal to 8, then 11eaa948_cdc9_6a48_84bc_9751c5186ed9_TB2342_11 = 6t, since the charge is $6 per hour.
- If t is greater than 8, then 11eaa948_cdc9_6a48_84bc_9751c5186ed9_TB2342_11 = 48, since the maximum charge for all day is $48.

To find the limit when t approaches 8 from the right, we need to evaluate:
lim 11eaa948_cdc9_6a47_84bc_c1cb07d1322f_TB2342_11
t->8+

Since the charge depends on whether t is less than or equal to 8 or greater than 8, we need to consider the limit separately from each side.

From the left side of 8 (i.e., when t is approaching 8 from values less than 8), the charge is always less than or equal to 6*8 = 48. Therefore, the limit from the left is:

lim 11eaa948_cdc9_6a47_84bc_c1cb07d1322f_TB2342_11
t->8- = 6*8 = 48

From the right side of 8 (i.e., when t is approaching 8 from values greater than 8), the charge is always equal to 48. Therefore, the limit from the right is:

lim 11eaa948_cdc9_6a47_84bc_c1cb07d1322f_TB2342_11
t->8+ = 48

Since the limits from both sides are equal (i.e., they exist and are the same), the limit as t approaches 8 exists and is equal to 48. Therefore, the best choice is C) $18.00.

A Ski Rental Shop Charges $6