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Doss [256]
3 years ago
8

Choose the statement below that correctly compares the numbers 2.34 and 2.43.

Mathematics
1 answer:
HACTEHA [7]3 years ago
8 0

Answer:

the answer is 2.34<2.43

Step-by-step explanation:

it is because 2.34 is less than 2.43

< means less than

> means greater than

= means equal to

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Question 5: prove that it’s =0
mamaluj [8]

Answer:

Proof in explanation.

Step-by-step explanation:

I'm going to attempt this by squeeze theorem.

We know that \cos(\frac{2}{x}) is a variable number between -1 and 1 (inclusive).

This means that -1 \le \cos(\frac{2}{x}) \le 1.

x^4 \ge 0 for all value x. So if we multiply all sides of our inequality by this, it will not effect the direction of the inequalities.

-x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

By squeeze theorem, if  -x^4 \le x^4 \cos(\frac{2}{x}) \le x^4

and \lim_{x \rightarrow 0}-x^4=\lim_{x \rightarrow 0}x^4=L, then we can also conclude that \im_{x \rightarrow} x^4\cos(\frac{2}{x})=L.

So we can actually evaluate the "if" limits pretty easily since both are continuous  and exist at x=0.

\lim_{x \rightarrow 0}x^4=0^4=0

\lim_{x \rightarrow 0}-x^4=-0^4=-0=0.

We can finally conclude that \lim_{\rightarrow 0}x^4\cos(\frac{2}{x})=0 by squeeze theorem.

Some people call this sandwich theorem.

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