- (a) 4; (b) 4; (c) 4
(a) Notice that f(x) is a piecewise function, which means that we use the function f(x) = x^2 − 5
for all values of x less than or equal to 3. Thus, f(x) = 3^2 − 5 = 4.
(b) Here we use the function f(x) = x + 1 for all values of x greater than 3. Thus, f(x) = 3 +
1 = 4.
(c) In order to evaluate the limit as x approaches 3, we find the limit as it approaches 3+ (from
the right) and the limit as it approaches 3− (from the left). If the two limits approach the same
value, or both approach positive infinity or both approach negative infinity, then the limit is that
value, or the appropriately signed infinity. If the two limits do not agree, the limit “Does Not
Exist.” Here, if we refer to the solutions in parts (a) and (b), we see that f(x) = 4 and
f(x) = 4. Because the two limits are the same, the limit is 4.
14.
Here, if we plug in for x, we get 3 cos x = 3 cos = .
15. 0
Here, if we plug in 0 for x, we get 3 = 3 = 3 = 0.
16. 3
Remember Rule No. 1, which says that = 1. If we want to find the limit of its
reciprocal, we can write this as = = = 1. Here, if we plug in 0 for x, we
get = (3)(1) = 3.
17.
