What is the limit as x approaches 4 of ((x^2-16))/(2-sqrt(x)) ?

The limit as x approaches 4 of ((x^2-16))/(2-sqrt(x)) is -32

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limit as x approaches 4 of ((x^2-16))/(2-sqrt(x))

x \to 4 lim (\frac{( x ^{2} - 16 )}{2 - x})

- 32

Solution steps

x \to 4 lim (\frac{x ^{2} - 16}{2 - x})

Rationalize denominator

\frac{x ^{2} - 16}{2 - x} : - (x + 4) (x + 2)

= x \to 4 lim (- (x + 4) (x + 2))

Plug in the value

x = 4

= - (4 + 4) (4 + 2)

Simplify

- (4 + 4) (4 + 2) : - 32

= - 32

\frac{d}{d x} (ln (2 e^{- x} sin (x)))

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g (x) = 6 - x

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What is the limit as x approaches 4 of ((x^2-16))/(2-sqrt(x)) ?
The limit as x approaches 4 of ((x^2-16))/(2-sqrt(x)) is -32