What is the value of # lim_(x rarr 0) a #, where #a# is a constant ?

Answer 1

# lim_(x rarr 0) a = a AA a in RR\ \ \ #, where #a# is a constant

We seek:

# lim_(x rarr 0) a \ \ \ #, where #a# is a constant

We note that if we define a function #f# by:

# f(x) =a#

Then as #a# is a constant, it is completely independent of the variable #x#, and is continuous over the entire domain #RR#. If we examine the behavior of #f(x)# then just to the left of #x=0# then #f(x)=a#, similarly to the right, and also at #x=0# we have #f(x)=a#.

So we have:

# lim_(x rarr 0^-) f(x) = lim_(x rarr 0^+) f(x) = lim_(x rarr 0) f(x) = a#

Hence

# lim_(x rarr 0) a = a AA a in RR\ \ \ #, where #a# is a constant

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Answer 2

Aurora Alvarado

The value of lim_(x rarr 0) a, where a is a constant, is equal to the constant value of a.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.