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Use a graph to find a number $ N $ such that

$$ \text{if} \hspace{5mm} x > N \hspace{5mm} \text{then} \hspace{5mm} \biggl| \frac{3x^2 + 1}{2x^2 + x + 1} - 1.5 \biggr| < 0.05 $$

$$

N=15

$$

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This is problem number seventy one of us to a calculus Eighth edition section to Prince six Is the graft to find a number in such that if X is greater than in, then the absolute value of the quantity three x worthless one, no matter where they wanted me to. X squared plus X plus one minus one point is less than zero point zero five. So we're going to use a graft. We're going to put this exact function here on the left side. This everything here within the emcee Valya, including now civility signs. We're going to compare it to the values zero point zero five. And if we do that here we have the function in the of the absolutely function in red. And we're comparing it with the y values zero point zero five. And if we would like this function Red Toby Ah, less than zero point zero five. Here we see that we must choose on and end value greater than or equal greater than fourteen point Tito for so in our case from our graph and is approximately fourteen point before. If fourteen point eight, if m is supposed to be an integer then when we would say is that thanks speaker to them. Fifteen. So fifteen is acceptable fourteen point game if it can be any number, is a bit more correct. Fourteen point oh four. But for our sake we'LL see the critics credit than fifteen guarantees that this and equality to the rate and satisfied.