clara1223
  • clara1223
find the limit as x approaches 3 of (1)/(x-3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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clara1223
  • clara1223
\[\lim_{x \rightarrow 3}\frac{ 1 }{ x-3 }\]
tkhunny
  • tkhunny
What does the denominator do as x approaches 3?
clara1223
  • clara1223
@tkhunny it becomes 0...?

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clara1223
  • clara1223
please help! i have this and one more limit problem and i'm done and ive been studying all day and im exhausted and I just don't understand these.
jim_thompson5910
  • jim_thompson5910
I suggest looking at a table of values specifically x values close to x = 3 like x = 3.1, x = 3.01, x = 3.001 and x = 2.99, x = 2.999, x = 2.9999, etc
jim_thompson5910
  • jim_thompson5910
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clara1223
  • clara1223
I already know that the limit doesnt exist I just need to know how to prove it
jim_thompson5910
  • jim_thompson5910
|dw:1441074140948:dw|
jim_thompson5910
  • jim_thompson5910
as x gets closer to 3 from the left side, the value of f(x) heads off to negative infinity so the left hand limit is equal to -infinity \[\Large \lim_{x \to 3^{-}}f(x) = -\infty\]
jim_thompson5910
  • jim_thompson5910
as x gets closer to 3 from the right side, the value of f(x) heads off to positive infinity the right hand limit is equal to +infinity \[\Large \lim_{x \to 3^{+}}f(x) = +\infty\]
jim_thompson5910
  • jim_thompson5910
LHL = left hand limit RHL = right hand limit since \[\Large LHL \ne RHL\] the limit at x = 3 itself does not exist the graph confirms this https://www.desmos.com/calculator/e09hafa0f1
clara1223
  • clara1223
@jim_thompson5910 how would I prove this algebraically? is there a way to manipulate or sinplify 1/x-3?
jim_thompson5910
  • jim_thompson5910
I don't know any way to prove it algebraically other than to use a table maybe
clara1223
  • clara1223
@tkhunny do you know of any way to prove it algebraically?
tkhunny
  • tkhunny
x - 3 = 0 -- Solve.

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