[tex]\lim_{x \to 5 }\frac{\sqrt{x-1}-2 }{x-5}[/tex]

Предыдущий
вопрос Следующий
вопрос

To find the limit of the function as x approaches 5, we need to first simplify the expression by multiplying both the numerator and the denominator by the conjugate of the numerator.

Conjugate of the numerator is obtained by changing the sign between the terms, so the conjugate of √(x-1) - 2 is √(x-1) + 2.

After multiplying by the conjugate, the expression becomes:

lim as x approaches 5 of ((√(x-1) - 2)(√(x-1) + 2))/(x-5)

= lim as x approaches 5 of ((x-1) - 4)/(x-5)

= lim as x approaches 5 of (x - 5)/(x-5)

= 1

Therefore, the limit of the function as x approaches 5 is 1.