High School

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The only thing we know about the function is that lim (x) x² = 2 . Use it to compute the following limits:
x → 0
lim (x)/x
x → 0

Answer :

By using the given limit information and simplifying the expressions, it is found that lim (x/x) as x approaches 0 is 1.

We are given that limx→0 x² = 2. To compute the limit of a different function involving x, we need to apply this given information.

Let's compute the limit:

limx→0 (x / x). Initially, substituting x = 0 results in the indeterminate form 0/0. To resolve this, consider simplifying the given limit:

limx→0 (1) because limx→0 (x / x) equals 1 as long as x ≠ 0.

Hence, the limit simplifies to:

limx→0 (x / x) = 1, assuming x ≠ 0.

This uses the property that the quotient of the same functions (except at x = 0) simplifies directly to 1.

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