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If f is a continuous function such that its limit as x approaches positive infinity is 5. Discuss the following limit: limit of f as x approaches negative infinity; for each condition below. If the limit exists find it. If not possible explain.

a) The graph of f is symmetric to the y-axis.

b) The graph of f is symmetric to the origin.

1 Answer
John D.
Jun 15, 2017

In case A, #lim_(x->-oo)f(x) = 5#.

In case B, #lim_(x->-oo)f(x) = -5#.

Explanation:

Case A

If the graph is symmetric to the y-axis, then this means that:

#f(x) = f(-x)#

Therefore, we can say that:

#lim_(x->-oo)f(x) #

#= lim_(x->oo)f(-x)#

# = lim_(x->oo)f(x) = 5#

Case B

If the graph is symmetric to the origin, then this means that:

#-f(x) = f(-x)#

Therefore, we can say that:

#lim_(x->-oo)f(x)#

#= lim_(x->oo)f(-x)#

#= - lim_(x->oo)f(x)#

#=-5#

Final Answer

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