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Finding Values that Satisfy a Limit

  • Thread starter eumyang
  • Start date
  • #1
eumyang
Homework Helper
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This may be a dumb question, but I'll ask anyway...

Homework Statement


Find the values of a and b such that
[itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]

Homework Equations


N/A

The Attempt at a Solution


I already have the work and the solution. However, someone showed me a different way. Here are the first couple of steps:
[itex]\lim_{x \rightarrow 0} \frac{\sqrt{a + bx} - \sqrt{3}}{x} = \sqrt{3}[/itex]
[itex]\lim_{x \rightarrow 0} \left( \sqrt{a + bx} - \sqrt{3} \right) = \sqrt{3} \cdot x[/itex]
[itex]\lim_{x \rightarrow 0} \sqrt{a + bx} = \sqrt{3} + \sqrt{3} \cdot x[/itex]
I'm having a brain fart. Is multiplying both sides by x, and then adding sqrt 3 to both sides, legal?
 

Answers and Replies

  • #2
Office_Shredder
Staff Emeritus
Science Advisor
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On the second line, the left hand side is a number, and the right hand side is a function of x. Does that sound like two things that are going to be equal to you?
 
  • #3
eumyang
Homework Helper
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That's what I thought -- I'm just too d***ed sleep-deprived. Thanks for the confirmation.
 

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