Answer:
The limit as x approaches 2 from the left of f(x) is 5
The limit as x approaches 2 from the right of f(x) is -2
Step-by-step explanation:
From the left, the coordinate graph shows a horizontal line crossing the y axis at five that ends at the open poing (2,5).
The limit as x approaches 2 from the left of f(x) is 5. Given that, from the left the graph approaches to 5.
From the right, the coordinate graph shoes a horizontal line starting at the open point (2, -2) and continues to the right.
The limit as x approaches 2 from the right of f(x) is -2. Given that, from the right the graph approaches to 5.
Answer:
[tex]\lim_{x \to 2^-}f(x)=5[/tex]
[tex]\lim_{x \to 2^+}f(x)=-2[/tex]
Step-by-step explanation:
The graph of f(x) is that of a piecewise function that is composed of 2 horizontal lines and a point.
Notice in the graph that:
[tex]f(x) = 5[/tex] if [tex]x <2[/tex]
[tex]f(x) = 1[/tex] if [tex]x = 2[/tex]
[tex]f(x) = -2[/tex] if [tex]x> 2[/tex]
We must find the limit on the left of 2 and on the right of 2.
When we find the limit on the left of 2 it means that x is a value infinitesimally smaller than 2. Then [tex]x <2[/tex] .
Since x is less than 2 then f(x) tends to 5.
So
[tex]\lim_{x \to 2^-}f(x)\\\\=\lim_{x \to 2^-}5 = 5[/tex]
When we find the limit on the right of 2, it means that x is a value infinitesimally larger than 2. Then [tex]x> 2[/tex].
Since x is greater than 2 then f(x) tends to -2.
So
[tex]\lim_{x \to 2^+}f(x)\\\\=\lim_{x \to 2^+}-2 = -2[/tex]
