SOLUTION: limit as x -> 3 (2sqrt(x+1)-4)/(2x^2-x-15)

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Question 1017903: limit as x -> 3
(2sqrt(x+1)-4)/(2x^2-x-15)
Found 2 solutions by Edwin McCravy, robertb:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
matrix%282%2C1%2Clim%2C%22x-%3E3%22%29%28%282sqrt%28x%2B1%29-4%5E%22%22%29%2F%282x%5E2-x-15%29%29

Multiply by the conjugate of the numerator or denominator
(whichever has the square root) over itself:

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

Use FOIL on the top:

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

Factor out common factor on top.
Factor quadratic in denominator.

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29

matrix%282%2C1%2Clim%2C%22x-%3E3%22%29%22%22=%22%22

%22%22=%22%22


%22%22=%22%22



%22%22=%22%22

%22%22=%22%22

%0D%0A%0D%0A4%2F88%0D%0A%0D%0A%22%22=%22%22

1%2F22

Edwin

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
You can also use L'Hopital's rule:
.
(The limit has the indeterminate form 0/0.)