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.