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

The limit as x approaches 3 of (2x-4)^4(x-2) is 16

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limit as x approaches 3 of (2x-4)^4(x-2)

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

16

Solution steps

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

Plug in the value

x = 3

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

Simplify

(2 \cdot 3 - 4)^{4} (3 - 2) : 16

= 16

x \to 4 lim (\frac{x ^{2} + 4}{5})

x \to \frac{π}{2} lim (\frac{3 cos ^{2} ( x )}{2 - 2 sin ( x )})

x \to \frac{π}{3} lim (\frac{1 - 2 cos ( x )}{π - 3 x})

x \to - 2 lim (3 x - 2)

x \to 0 lim ((csc (x))^{x})

What is the limit as x approaches 3 of (2x-4)^4(x-2) ?
The limit as x approaches 3 of (2x-4)^4(x-2) is 16