Limit of a graph

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) = x√(7-x^-2)

A) lim f(x)  x→0⁻

B) lim  f(x) x→0⁺

Answer 1

Looking at Doug C.'s graph, you can easily see that the graph never approaches 0 from either direction, therefore the limit does not exist from the left or from the right.

Thinking of this algebraically, you need to pick a point that is close to 0 on each side and see what value y is approaching. From the right, I'll use x = 0.1

Since we cannot take the square root of a negative, the graph does not exist at this point. From the left, we could use x = -0.1. which yields that same results.

 

 

So from either direction, the limit does not exist.

Answer 2

f(x) = x√(7-x^-2)

A) lim f(x) x→0⁻

^{= 0}

B) lim  f(x) x→0⁺

^{= 0}