What is the limit as x approaches 2 of (3x-1)^{x^2-3x+4} ?

The limit as x approaches 2 of (3x-1)^{x^2-3x+4} is 25

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limit as x approaches 2 of (3x-1)^{x^2-3x+4}

x \to 2 lim ((3 x - 1)^{x^{2} - 3 x + 4})

25

Solution steps

x \to 2 lim ((3 x - 1)^{x^{2} - 3 x + 4})

Plug in the value

x = 2

= (3 \cdot 2 - 1)^{2^{2} - 3 \cdot 2 + 4}

Simplify

(3 \cdot 2 - 1)^{2^{2} - 3 \cdot 2 + 4} : 25

= 25

What is the limit as x approaches 2 of (3x-1)^{x^2-3x+4} ?
The limit as x approaches 2 of (3x-1)^{x^2-3x+4} is 25