Question

Does this limit exist?
lim 1-sqrt(1-x^2)
-----------
x->0 x
If yes, the limit is what?

Answer 1

I don't think it exists..

Answer 2

I have tried to calculate it through web calculator and found the limit is 0
Can everyone tell me why?

Answer 3

To answer the question, you have to multiply by the conjugate. Multiply top and bottom by (1+sqrt(1-x^2)). That's the trick to solving this type.

Answer 4

Yes. It works. You end up with x^2/(x + x (sqrt(1-x^2))). cancel an x from each term. Then sub in x = 0 to get a limit of 0.

Answer 5

Math is full of tricks. It's like having a tool box. There are questions that can't be solved if you don't have the right trick. Look up about the conjugate.

Answer 6

@jam333 but the numerator is still 0 after considering conjugate of sqrt(1-x^2)

Answer 7

Curse me and my laziness.

Answer 8

i would!
but cursing is not allowed here :P

Answer 9

frank,
did you simplify the numerator after multiplying by the conjugate ?

Answer 10

o i am so stupid XD

Answer 11

@hartnn thanks a lot

Answer 12

Sorry Sir.
But yea, after simplifying you should get it.

Answer 13

you're welcome ^_^
oh, and since you are new here,
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Have fun learning with Open Study! :)

Answer 14

Yes the numerator is 0 but the denominator is 1. 0/1 is 0. The limit is 0.