SOLUTION: Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 5 as x approaches 5 from the left . (2 points) 1 ; no

Algebra ->  Trigonometry-basics -> SOLUTION: Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 5 as x approaches 5 from the left . (2 points) 1 ; no      Log On


   

Question 1139241: Use graphs and tables to find the limit and identify any vertical asymptotes of limit of 1 divided by the quantity x minus 5 as x approaches 5 from the left . (2 points)

1 ; no vertical asymptotes

-∞ ; x = 5

∞ ; x = -5

-∞ ; x = -5
Found 2 solutions by MathLover1, Theo:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
lim%28x-%3E5%2C%281%2F%28x-5%29%29%29

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Limit from the left:
lim%28x-%3E5%2C%281%2F%28x-5%29%29%29+=+1%2F0=-infinity

answer: -infinity ; x+=+5

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the equation is 1 / (x-5)

there will be a vertical asymptote at x = 5.

as x approaches 5 from the left, the value of y gets more and more negative.

as x approaches 5 from the right, the value of y gets more and more positive.

you want to know the value of y as x approaches from the left.

the value of y gets more and more negative as x approaches 5 from the left, which makes the value of y approaching negative infinity.

that would make your solution as:

minus infinity; x = 5

here's my graph.

$$$

without the graph, you would take values of x very close to 5 from the left and values of x very close to 5 from the right and see which way they are going.

for example:

1 / (4.9999 - 5) = -10000
1 / (4.99999999 - 5) = -100000000

it's getting more and more negative.

1 / (5.0001 - 5) = 1000
1 / (5.00000001 - 5) = 100000000

it's getting more and more positive.