What is the limit as x approaches 1 of (x-1)/(sqrt(x+24)-5) ?

The limit as x approaches 1 of (x-1)/(sqrt(x+24)-5) is 10

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limit as x approaches 1 of (x-1)/(sqrt(x+24)-5)

x \to 1 lim (\frac{x - 1}{x + 24 - 5})

10

Solution steps

x \to 1 lim (\frac{x - 1}{x + 24 - 5})

Rationalize denominator

\frac{x - 1}{x + 24 - 5} : x + 24 + 5

= x \to 1 lim (x + 24 + 5)

Plug in the value

x = 1

= 1 + 24 + 5

Simplify

1 + 24 + 5 : 10

= 10

What is the limit as x approaches 1 of (x-1)/(sqrt(x+24)-5) ?
The limit as x approaches 1 of (x-1)/(sqrt(x+24)-5) is 10