SOLUTION: Solve x^2+x/x+1 as x approaches -1)

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Question 179377: Solve x^2+x/x+1
as x approaches -1)
Found 2 solutions by jim_thompson5910, solver91311:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
I assume that you want to evaluate the limit as x approaches -1

lim%28x-%3E-1%2C%28x%5E2%2Bx%29%2F%28x%2B1%29%29 Start with the given limit


lim%28x-%3E-1%2C%28x%28x%2B1%29%29%2F%28x%2B1%29%29 Factor out the GCF x


lim%28x-%3E-1%2C%28x%2Across%28%28x%2B1%29%29%29%2Fcross%28%28x%2B1%29%29%29 Cancel out like terms


lim%28x-%3E-1%2C%28x%29%29 Simplify


-1 Take the limit of x as x approaches -1. In other words, simply plug in x=-1


So lim%28x-%3E-1%2C%28x%5E2%2Bx%29%2F%28x%2B1%29%29=-1


Note: If you use a calculator to make the table of f%28x%29=%28x%5E2%2Bx%29%2F%28x%2B1%29, you'll see that x=-1 is NOT defined, but f%28x%29 values near that value get close to -1.

Answer by solver91311(12126) About Me  (Show Source):
You can put this solution on YOUR website!


I think you mean to evaluate

You need to use L'Hôpital's Rule:

If and then if the derivitives exist.

So:

If then and,

If then

and so:



John