lim _(xarrow 2)(sqrt (2x-3)-1)/(x-2)=

Question

Answer 1

To evaluate the limit

, we can use algebraic manipulation and L'Hôpital's Rule.First, let's rewrite the expression:

We notice that direct substitution of

results in an indeterminate form

. To resolve this, we can multiply the numerator and the denominator by the conjugate of the numerator:

The numerator simplifies as follows:

So the expression becomes:

We can factor the numerator:

Thus, the expression simplifies to:

Now, we can substitute

into the simplified expression:

Therefore, the limit is:

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