Question

Find limit as x approaches one of f of x for f of x equals the piecewise function 3 x minus 1 when x is less than or equal to one or 2 x squared when x is greater than one.

Answer 1

We are given that:
f(x) = 3x - 1 when x is less than or equal to 1 ..........> equation I
f(x) = 2x^2 when x is greater than 1 .............> equation II

Now, we need to calculate the limit as x approaches 1. To do so, we will substitute the value of x with one in the function that is valid at x=1
(equation I) as follows:
Limit as x approaches 1 = f(x) at x=1
Limit as x approaches 1 = 3(1) - 1 = 3-1 = 2