What is the limit as x approaches 0 of ((484+x)^{0.5}-22)/x ?

The limit as x approaches 0 of ((484+x)^{0.5}-22)/x is 1/44

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limit as x approaches 0 of ((484+x)^{0.5}-22)/x

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

\frac{1}{44}

Decimal

0.02272 \dots

Solution steps

x \to 0 lim (\frac{( 484 + x ) ^{0.5} - 22}{x})

Multiply by the conjugate of

(484 + x)^{0.5} - 22 : \frac{x}{( 484 + x ) ^{0.5} + 22}

= x \to 0 lim (\frac{\frac{x}{( 484 + x ) ^{0.5} + 22}}{x})

Simplify

\frac{\frac{x}{( 484 + x ) ^{0.5} + 22}}{x} : \frac{1}{( x + 484 ) ^{\frac{1}{2}} + 22}

= x \to 0 lim (\frac{1}{( x + 484 ) ^{\frac{1}{2}} + 22})

Plug in the value

x = 0

= \frac{1}{( 0 + 484 ) ^{\frac{1}{2}} + 22}

Simplify

\frac{1}{( 0 + 484 ) ^{\frac{1}{2}} + 22} : \frac{1}{44}

= \frac{1}{44}

What is the limit as x approaches 0 of ((484+x)^{0.5}-22)/x ?
The limit as x approaches 0 of ((484+x)^{0.5}-22)/x is 1/44