lim _(xarrow 0)(sqrt [4](x^4+1)-sqrt (x^2+1))/(x^2)

Question

Answer 1

To evaluate the limit

, we can use L'Hôpital's Rule since it is in an indeterminate form

.First, let's rewrite the expression:

We need to apply L'Hôpital's Rule, which states that if \(\lim_{x \to c} \frac{f(x)}{g(x)}\) results in

or

, then:

First, we find the derivatives of the numerator and the denominator.The numerator is

.Let

and

.Then, the derivatives are:

Now, applying L'Hôpital's Rule:

Simplify the expression:

As

:

Therefore, the limit is:

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