Question

Find each limit. Include a table of values to illustrate your answer. Include two tables if you need to consider a two sided limit.

Answer 1

lim (1+x)^1/x as x--> 0

Answer 2

Okay what do you believe the limit to be?

Answer 3

1? i am not really sure though

Answer 4

@ceb105

Answer 5

Yes you are correct, the limit=1, your question would like you to explain this by putting in values around x=0, so input values of x=0.1, 0.01, 0.001 etc. Do this from both the above and below (positive a negative x values) to adequately show it.

Alternatively, you know that Lim[x] x->0 = 0 therefore 1+Lim[x] x->0 = 1
=> Lim[1+x] x-> 0 = 1
1^n where n is any real number will be 1. Thus as it will tend to 1 from above and below, the limit is 1