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

The limit as x approaches 1/3 of (2-3x)^2+1 is 2

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limit as x approaches 1/3 of (2-3x)^2+1

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

2

Solution steps

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

Plug in the value

x = \frac{1}{3}

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

Simplify

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

= 2

x \to - 5 lim (x^{2} - 6)

x \to \frac{5}{3} lim (x^{3} - 2 x + 3)

θ \to 0 lim (\frac{( sin ( 2 θ ) )}{θ})

x \to 0 + lim ((3 x)^{x^{2}})

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

What is the limit as x approaches 1/3 of (2-3x)^2+1 ?
The limit as x approaches 1/3 of (2-3x)^2+1 is 2