# How do you write the Simpson’s rule and Trapezoid rule approximations to the #intsinx/x# over the inteval [0,1] with #n=6#?

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Simpson's Rule: [ \text{Approximation using Simpson's Rule} = \frac{\Delta x}{3} \left[ f(x_0) + 4f(x_1) + 2f(x_2) + 4f(x_3) + 2f(x_4) + 4f(x_5) + f(x_6) \right] ]

Trapezoid Rule: [ \text{Approximation using Trapezoid Rule} = \frac{\Delta x}{2} \left[ f(x_0) + 2f(x_1) + 2f(x_2) + 2f(x_3) + 2f(x_4) + 2f(x_5) + f(x_6) \right] ]

Given (n = 6), the interval ([0,1]) is divided into 6 equal subintervals, hence (\Delta x = \frac{1-0}{6} = \frac{1}{6}). Therefore, (x_0 = 0), (x_1 = \frac{1}{6}), (x_2 = \frac{1}{3}), (x_3 = \frac{1}{2}), (x_4 = \frac{2}{3}), (x_5 = \frac{5}{6}), and (x_6 = 1).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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