Question

In the following, determine whether a particular limit exists, is infinite, or neither.

a)limx→3(x²-9x-3)
b)limx→0sin(x)/∣x∣

a) (a) Infinite, (b) Infinite
b) (a) Infinite, (b) Does not exist
c) (a) 12, (b) 1
d) (a) Does not exist, (b) 0

Answer 1

In part (a), the limit does not exist. In part (b), the limit also does not exist.

Step-by-step explanation:

In the given question, we are asked to determine whether the limits in parts (a) and (b) exist, are infinite, or neither.

a) limx→3(x²-9x-3)

To find the limit, we substitute the value x = 3 into the expression:

limx→3(3²-9(3)-3) = limx→3(9-27-3) = limx→3(-21)

Since the expression doesn't approach a finite value as x approaches 3, the limit does not exist.

b) limx→0sin(x)/∣x∣

To find the limit, we consider the right-hand limit and the left-hand limit separately:

limx→0+sin(x)/∣x∣ = 1/0 = ∞ (Approaches infinity)

limx→0-sin(x)/∣x∣ = -1/0 = -∞ (Approaches negative infinity)

Since the right-hand limit and the left-hand limit are not equal, the limit does not exist.