Limit Using Conjugates: Square Root in Denominator, Limit Using Conjugates Playlist

In this video, Prof. Happy Strawberry from the F.I.T. Department of Mathematics solves a limit where the square root appears in the denominator: \lim_{x\to 0}\frac{x}{\sqrt{1+x}-1} We begin with direct substitution and again get the indeterminate form 0/0. But this time, the square root is not in the numerator, it’s in the denominator. The key idea: Multiply by the conjugate of the denominator We go step by step: * Identify the conjugate \sqrt{1+x}+1 * Multiply numerator and denominator * Use the difference of squares * Cancel the common factor * Simplify and evaluate This example shows how flexible the conjugate method is , it works no matter where the root appears.