Question

calculate lim3/(1+x) as x approaches to the left hand limit of -1.

Answer 1

-infty
we know the function does not exist at -1

you could just plug in some close number to the left of -1 to see if the infinity will be the negative kind or the positive kind

Answer 2

I need to know the process of how to solve. Not just plugging.

Answer 3

If you plug in x =-1, then you get 3/(1-1) = 3/0 which is undefined


However, you can plug in a slightly smaller value (say x = -1.1) to get 3/(1-1.1) = -30


If you keep getting closer to -1, and plug in x = -1.01, you get 3/(1-1.01) = -300


If you keep going and you plug in successive values of x that keep getting closer and closer to -1 (and they're all smaller than -1), then you'll find that the expression will become larger and larger in the negative direction.


So as x --> -1 from the left, 3/(1+x) --> -infinty