Question

Evaluate the limit using the appropriate Limit Law(s). (If an answer daes riot exist, enter DNE,) \[ \lim _{x \rightarrow 2} \sqrt{\frac{2 x^{2}+1}{3 x-2}} \] 26

Answer 1

To evaluate the limit
`\displaystyle\sf \lim_(x\to 2) \sqrt{(2x^(2)+1)/(3x-2)}`, we can directly substitute
`\displaystyle\sf x=2` into the expression.

Plugging in
`\displaystyle\sf x=2`, we have:

`\displaystyle\sf \lim_(x\to 2) \sqrt{(2x^(2)+1)/(3x-2)} = \sqrt{(2(2)^(2)+1)/(3(2)-2)} = \sqrt{(2(4)+1)/(6-2)} = \sqrt{(9)/(4)} = (3)/(2)`.

Therefore, the limit is
`\displaystyle\sf (3)/(2)`.