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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.
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
In case A,
In case B,
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
