What is the limit as x approaches 3+of (x^2-9)^{x-3} ?

The limit as x approaches 3+of (x^2-9)^{x-3} is (3^2-9)^3(3^2-9)^{-3}

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limit as x approaches 3+of (x^2-9)^{x-3}

x \to 3 + lim ((x^{2} - 9)^{x - 3})

(3^{2} - 9)^{3} (3^{2} - 9)^{- 3}

Solution steps

x \to 3 + lim ((x^{2} - 9)^{x - 3})

Simplify

(x^{2} - 9)^{x - 3} : (x^{2} - 9)^{x} (x^{2} - 9)^{- 3}

= x \to 3 + lim ((x^{2} - 9)^{x} (x^{2} - 9)^{- 3})

Plug in the value

x = 3

= (3^{2} - 9)^{3} (3^{2} - 9)^{- 3}

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What is the limit as x approaches 3+of (x^2-9)^{x-3} ?
The limit as x approaches 3+of (x^2-9)^{x-3} is (3^2-9)^3(3^2-9)^{-3}