Calculus Question

Question

Given the piecewise function:

f(x) = x^2+3x+1, x > 1, x can't equal 2

f(x) = 2, x < or equal to 1

determine the value of the limit as x approaches 2

A) undefined

B) 11

C) 2

D) 4

Help!? Is it A?

Answer 1

There are 2 limits, when x→2- and when x→2+.  In the neighborhood of x = 2, you are in the region where

 

f(x) = x² + 3x + 1

 

So whether you approach 2 from the left or the right, the limit approaches  2² + 3(2) + 1 = 11

 

lim_x→2+ f(x) = 11

 

lim_x→2- f(x) = 11

 

Since the 2 limits are equal, the limit at x = 2 is defined, and equal to 11.

Answer 2

It is removable discontinuity at x=2.

11