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

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

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

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

\frac{3}{2}

Decimal

1.5

Solution steps

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

Plug in the value

x = 2

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

Simplify

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

= \frac{3}{2}

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