Asked by Janet
                If a function f(x) is continuous, then what can be said about the value of the following limit
lim-->2 [f(x) +4x]
            
        lim-->2 [f(x) +4x]
Answers
                    Answered by
            Janet
            
    I figured this out this way but am not sure it's right.  
f(2) + 4(2) = f(2) + 8. From this we can tell that it exists, but I'm not sure why.
    
f(2) + 4(2) = f(2) + 8. From this we can tell that it exists, but I'm not sure why.
                    Answered by
            MathMate
            
    If f(x) is continuous (on ℝ), then f(2) must exist.  Also, it is known that polynomials are continuous on ℝ.
Within these constraints, limits are additive, so
Lim x->2 f(x)+4x
=Lim x->2 f(x) + Lim x->2 4x
=f(2) + 4(2)
=f(2) + 8,
as you have found.
    
Within these constraints, limits are additive, so
Lim x->2 f(x)+4x
=Lim x->2 f(x) + Lim x->2 4x
=f(2) + 4(2)
=f(2) + 8,
as you have found.
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