- #1

kreil

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[tex]\lim_{x{\rightarrow}0}\frac{\sqrt{1+2x}-\sqrt{1+3x}}{x+2x^2}[/tex]

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- Thread starter kreil
- Start date

- #1

kreil

Gold Member

- 669

- 68

[tex]\lim_{x{\rightarrow}0}\frac{\sqrt{1+2x}-\sqrt{1+3x}}{x+2x^2}[/tex]

- #2

courtrigrad

- 1,236

- 1

Use L'Hopitals Rule.

- #3

StatusX

Homework Helper

- 2,571

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Or you could multiply by the conjugate of the numerator. (ie, sqrt(1+2x)+sqrt(1+3x)).

- #4

JasonRox

Homework Helper

Gold Member

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If you haven't learned L'Hopitals Rule, I recommend to learn it and use it to check your answer

Also, you can always test it numerically. I do that sometimes just to be 100% certain. I would try something like x=0.01, 0.001 and 0.0001.

- #5

calcnd

- 20

- 0

As stated above, L'Hopital's rule, or, if that's not allowed, rationalize the numerator.

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