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]

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.
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.

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