Limit Using Conjugates: Flipped Square Root Case, Limit Using Conjugates Playlist

In this video, Prof. Happy Strawberry from the F.I.T. Department of Mathematics solves another limit using the conjugate trick , but with a slightly different structure: \lim_{x\to 1}\frac{1-\sqrt{x}}{1-x} We start with direct substitution and again get the indeterminate form 0/0. This time, the square root appears in a different position, but the same strategy applies: Multiply by the conjugate We go step by step: * Identify the conjugate 1 + \sqrt{x} * Multiply numerator and denominator * Use the difference of squares * Cancel the common factor * Simplify and evaluate This example shows that the conjugate method works even when the expression looks reversed.