Question

Evaluate the limits below where possible:

lim x→a f(x) = 0
lim x→a g(x) = 0
lim x→a h(x) = 1
lim x→a p(x) = [infinity]
lim x→a q(x) = [infinity]

Answer 1

The limits given are for different functions, some of which approach a finite number and some approach infinity.

Step-by-step explanation:

The limits given are:

• lim x→a f(x) = 0
• lim x→a g(x) = 0
• lim x→a h(x) = 1
• lim x→a p(x) = ∞ (infinity)
• lim x→a q(x) = ∞ (infinity)

For the limits where the function approaches a finite number, such as f(x) and g(x), the limit is equal to the value of the function at that point. Therefore, lim x→a f(x) = 0 and lim x→a g(x) = 0.

For the limits where the function approaches infinity, such as p(x) and q(x), the limit is represented by the symbol ∞ (infinity). As x approaches a certain value, the function grows without bound. Therefore, lim x→a p(x) = ∞ and lim x→a q(x) = ∞.