Question

Pre-calc, image attached

Answer 1

`\lim_(x \to \(-1) f(x)=-2`

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