6.119. lim _(xarrow infty )((7x^10-3)/(7x^10)+2)^-2x^(10)

Question

Answer 1

To solve this limit, we can use the fact that as

approaches infinity, the dominant term in the numerator and denominator will be the highest power of

. In this case, the dominant term in both the numerator and denominator is

.We can rewrite the expression as:

First, let's simplify the fraction inside the limit:

However, we need to be more precise. Let's factor out

from the numerator and denominator:

As

,

and

approach 0, so:

Thus, the limit simplifies to:

Since

:

Therefore, the correct answer is:

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