Have tried to multiplicate with the conjugate.
A conjugate limit is used to evaluate the limit of a function that may otherwise be undefined or indeterminate at a certain point. By manipulating the function with its conjugate, we can simplify the expression and find the limit more easily.
The conjugate of a function is found by changing the sign between the two terms in the numerator, i.e. changing a plus sign to a minus sign, or vice versa. For example, the conjugate of $\frac{\sqrt{x}-1}{x-1}$ would be $\frac{\sqrt{x}+1}{x-1}$.
A conjugate limit should be used when evaluating the limit of a function that contains a radical in the numerator, as in the case of $\frac{\sqrt{x}-1}{x-1}$. It can also be used when evaluating the limit of a rational function with a complex denominator, such as $\frac{x+1}{x^2+1}$.
No, a conjugate limit can only be used for certain types of limits, specifically those involving radicals or complex denominators. It cannot be used for limits involving trigonometric functions or exponential functions, among others.
If a limit involves a radical in the numerator or a complex denominator, then a conjugate limit can typically be used. However, it is always best to check the limit using other methods first, such as direct substitution or L'Hopital's rule, before resorting to a conjugate limit.