Sarthaks Test
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Evaluate the following limit : \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{3-\text x}-1}{2-\text x}\)

lim(x→2)(√(3- x)- 1)/(2 -x)

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Given \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{3-\text x}-1}{2-\text x}\)

To find: the limit of the given equation when x tends to 2

Substituting x as 2, we get an indeterminant form of \(\cfrac00\)

Rationalizing the given equation

Formula: (a + b) (a - b) = a2 - b2

Now we can see that the indeterminant form is removed, so substituting x as 2

We get \(\lim\limits_{\text x \to 2}\cfrac{\sqrt{3-\text x}-1}{2-\text x}\) = \(\cfrac1{1+1}=\cfrac12\)

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