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Determine the values of $x$ for which the quadratic approximation $f(x) \approx T_{2}(x)$ in Example 7 is accurate to within 0.1 $\left[$ Hint: Graph $y=T_{2}(x), y=\cos x-0.1,$ and \right. $y=\cos x+0.1$ on a common screen. $]$
$-1.261< x <1.261$
Calculus 1 / AB
Chapter 3
Derivatives
Section 8
Linear Approximations and Taylor Polynomials
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University of Nottingham
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Lectures
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In this problem, we are asked to determine the x for which the approximation, in example, 7, is accurate to wooden into so mathematically. We can write this form as the sine x minus 1 minus 1. Half x square is accurate within .1, where this part is our either polynomial order 2. So this equation, we say this equal is less say. This is 1, is same as cosine x, minus .11 minus 1, half x square cosine, x, plus point to the initial. In the first negro of these same as the second 1, now, if we solve for the values of x, that satisfies basicalty, we find x, 1.2 6 point now, if we sold for the values of x that satisfies now. This part that we find x to be negative 1.26, so we're going to say when x is when x is between negative 1.26 and positive 1.26. Then the approximation is accurate to with .1.
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