What Is the Value of b for the Limit to Exist?

[Meeker]

Homework Statement

Determine the value of b so that each limit exists.

lim (4x^2 + 11x -3) / (x-b)
x->b

Homework Equations

The Attempt at a Solution

I factored it to (4x-1)(x+3) / (x-b) but still not too sure what else to do.

 

[Mark44]

Homework Statement

Determine the value of b so that each limit exists.

lim (4x^2 + 11x -3) / (x-b)
x->b

Homework Equations

The Attempt at a Solution

I factored it to (4x-1)(x+3) / (x-b) but still not too sure what else to do.

In order for the limit to exist, the discontinuity caused by dividing by x - b has to be removable. This means that there must also be a factor of x - b in the numerator.