Decide whether the limit exists. If it exists, find its value.lim f(x)x→1

f (x) ={ 1x−1 if x 6 = 1;0 if x = 1.(a) Does limx→5f (x) exist? If so, what is it? Try and establish thevalidity of your answer formally using an epsilon-delta argument.If it exists, does it equal f (5)? Is this function continuous at thepoint x = 5?(b) Does limx→1f (x) exist? If so, what is it? Try and establish thevalidity of your answer formally using an epsilon-delta argument.If it exists, does it equal f (1)? Is this function continuous at thepoint x = 1?(c) Is this function continuous?2. Consider the functionf (x) ={x2 if x 6 = 0;−50 if x = 0.2

Evaluate the limit, if it exists. (If it does not exist, enter NONE).

Use the graph of f to estimate each limit, or write und (meaning undefined) if no limit exists. Use inf for ∞.limx→1−f(x)= limx→1+f(x)= limx→1f(x)=

Evaluate the limit:lim𝑥→2𝑥−2𝑥2−4=

The Limit of a Function