Limit Using Conjugates: Two Square Roots, Limits Using Conjugates Playlist

In this video, Prof. Happy Strawberry from the F.I.T. Department of Mathematics solves a more advanced limit using the conjugate method: \lim_{x\to 0}\frac{\sqrt{1+x}-\sqrt{1-x}}{x} We start with direct substitution and again obtain the indeterminate form 0/0. But this time, the numerator contains two square roots connected by subtraction. The key strategy: multiply by the conjugate to eliminate both roots at once. We go step by step: * Identify the conjugate expression * Multiply numerator and denominator * Use the difference of squares carefully * Simplify the algebra * Cancel the common factor * Evaluate the limit This is a classic and very important limit pattern in calculus.