Question

Use the graph of the function f to state the value of each limit, if it exists. (If an answer does not exist, enter DNE.)

f(x) = 81 + e1/x
(a)
lim
x?0?f(x)

(b)
lim
x?0+f(x)

(c) lim
x?0f(x)

Answer 1

The question is about finding the limits of a function as x approaches zero from both sides, but without the graph or equation of f(x), it is impossible to provide the limits requested.

Step-by-step explanation:

The student is asking about limits of a function as x approaches zero from different directions. Unfortunately, the description provided does not include the actual graph or functional form of f(x), which is essential for determining the limits. However, in general:

• (a) ℓ x→0- f(x): This represents the limit of the function f(x) as x approaches zero from the left side. Without the function's graph or equation, we can't determine this limit.
• (b) ℓ x→0+ f(x): This represents the limit of f(x) as x approaches zero from the right side. As with the previous limit, we need the graph or equation to find this limit.
• (c) ℓ x→0 f(x): This refers to the overall limit as x approaches zero from both sides. If the left-hand limit and the right-hand limit are different, the overall limit does not exist (DNE).

It's important to analyze the graph or the equation of f(x) to accurately determine these limits.