Help Me Find the Limit

Question

lim_x→2 -2x³ -4x² +2x +4

How do you find limits when given equations like this one?

Answer 1

Plug in x=2. All polynomials are continuous and the definition of continuity is that the value of the function = the limit at all points.

Generally speaking, to evaluate a limit as x approaches a, start by plugging in x = a. If the expression is defined, that is the limit.

Limits prove more useful for functions that are undefined at x = a, but have a limit as x approaches a. One tremendously important such expression in calculus is the difference quotient, the limit of which defines instantaneous rate of change of a function at that point.