Suppose that limx1 fx 3 Show that limx1 fx 1 4 Using the

Suppose that lim(x1) f(x) = 3. Show that lim(x1) f(x) + 1 = 4. Using the definition of convergence

Solution

lim (x----->1) f(x)=3 so for

e>0, there exist ,d, so that:

|f(x)-3|<d for all |x-1|<e

Let e >0

|f(x)+1-4|=|f(x)-3|<d as shown above for all |x-1|<e

Hence,

lim(x--->1) f(x)+1=4