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Archy [21]
3 years ago
15

The product of 4 and a number plus 17 is 5

Mathematics
2 answers:
Anton [14]3 years ago
7 0
The equation should be 4x+17=5
dalvyx [7]3 years ago
4 0
The number is -3 and the equation should be 4x+17=5
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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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