f(x) = {x^3 - 1, x> or equal to -1
{2x,x<-1
find limit x->-1 f(x)
What steps do I follow to solve the limit of the piecewise function?
To solve the limit of the given piecewise function, follow these steps:
1. Start by evaluating the limit from the left-hand side (x approaching -1 from the negative side).
- For the given function, when x<-1, the function is f(x) = 2x. So, plug in x = -1 into this expression: f(x) = 2(-1) = -2.
2. Next, evaluate the limit from the right-hand side (x approaching -1 from the positive side).
- For the given function, when x>=-1, the function is f(x) = x^3 - 1. So, plug in x = -1 into this expression: f(x) = (-1)^3 - 1 = -1 - 1 = -2.
3. Finally, compare the values of the left and right limits.
- Since the limits from both the left and right sides are equal, the overall limit exists and is equal to the value, which is -2.
Therefore, the limit of the piecewise function f(x) as x approaches -1 is -2.