What is the limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4) ?

The limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4) is 4/5

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limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4)

x \to 1 lim (\frac{( 26 - x - 5 )}{17 - x - 4})

\frac{4}{5}

Decimal

0.8

Solution steps

x \to 1 lim (\frac{26 - x - 5}{17 - x - 4})

Rationalize denominator

\frac{26 - x - 5}{17 - x - 4} : \frac{( 26 - x - 5 ) ( 17 - x + 4 )}{- x + 1}

= x \to 1 lim (\frac{( 26 - x - 5 ) ( 17 - x + 4 )}{- x + 1})

Multiply by the conjugate of

26 - x - 5 : \frac{- x + 1}{26 - x + 5}

= x \to 1 lim (\frac{\frac{- x + 1}{26 - x + 5} ( 17 - x + 4 )}{- x + 1})

Simplify

\frac{\frac{- x + 1}{26 - x + 5} ( 17 - x + 4 )}{- x + 1} : \frac{- x + 17 + 4}{- x + 26 + 5}

= x \to 1 lim (\frac{- x + 17 + 4}{- x + 26 + 5})

Plug in the value

x = 1

= \frac{- 1 + 17 + 4}{- 1 + 26 + 5}

Simplify

\frac{- 1 + 17 + 4}{- 1 + 26 + 5} : \frac{4}{5}

= \frac{4}{5}

What is the limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4) ?
The limit as x approaches 1 of ((sqrt(26-x)-5))/(sqrt(17-x)-4) is 4/5