Answer:
[tex]\lim_{x \to \(-1} f(x)=-2[/tex]
Step-by-step explanation:
In order for a limit to exist in a piecewise function, both its right-side and left-side limits must be equal to each other:
- So, if we plug in x=-1 for the left side limit, we get 2cos(πx) = 2cos(π(-1)) = 2cos(-π) = 2(-1) = -2
- Plugging in x=-1 for the right-side limit, we get 2/cos(πx) = 2/cos(π(-1)) = 2/cos(-π) = 2/(-1) = -2
- Since both the right-side and left-side limits are equal to each other, we can say that the limit of f(x) as x approaches -1 is -2, therefore the limit exists
- See the attached graph
