\ \

The sequence is . \ \

(a) \ \

Substitute in . \ \

\ \

\ \

\ \

. \ \

Therefore, . \ \

\ \

(b) \ \

The sequence is . \ \

\ \

If the value of is increasing the value of is increasing for . \ \

for all values of . \ \

Therefore, the terms are decreasing. \ \

\ \

(c) \ \

The sequence is . \ \

As the value of tends to the value of tends to . \ \

Therefore, the factorial function grows faster than the exponential function for the same base. \ \

\ \

(a) . \ \

(b) The terms are decreasing. \ \

(c) The factorial function grows faster than the exponential function for the same base.