To determine the value of b for the limit lim (4x^2 + 11x - 3) / (x - b) as x approaches b to exist, the numerator must contain the factor (x - b). The expression can be factored as (4x - 1)(x + 3) / (x - b). For the limit to be defined, b must equal -3, which is the root of the numerator that cancels the discontinuity at x = b.
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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.Meeker said: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.