lim _(x arrow 3) f(x)=(x^3-3 x^2-2 x+6)/(x-3)

To find the limit of the given function as approaches 3, we can try to simplify the expression. Let's factor the numerator: We can use polynomial division or synthetic division to divide by . Let's use synthetic division:```3 | 1 -3 -2 6 | 3 0 -6 ---------------- 1 0 -2 0```The quotient is , so we can rewrite the function as: Now, we can find the limit as approaches 3: Therefore, the limit of the given function as approaches 3 is 7.