Question

Hey, can someone help me out with this calculus problem? I'm stuck here.

lim (sqrt(1+x)-sqrt(1-x))/x as x->0

Do I times the numerator and denominator by sqrt(1+x)-sqrt(1-x)?

Answer 1

multiply denominator and numerator by sqrt(1+x) + sqrt(1-x)

Answer 2

Thank you, I'll try that now. So it was just reversing the the negative sign to positive I see.

Answer 3

The reasoning is like what you learned in elementary algebra: $$(a+b)(a-b)=a^2-b^2$$

Answer 4

^ Yeah

Answer 5

We want to get rid of radicals in our numerator to see if it simplifies; so we can multiply $$(\sqrt{1+x}-\sqrt{1-x})(\sqrt{1+x}+\sqrt{1-x})=(\sqrt{1+x})^2-(\sqrt{1-x})^2$$

Answer 6

Ahh, I see now. Thanks for explaining that