Let f(x) = (1 + x)1⁄x.(a)Estimate the value of the limit lim x→0 (1 + x)1⁄x to five decimal places.

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

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

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)=

Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x→0.2− 5x − 1|5x3 − x2|

(a) limx→1x2 − 1x − 1