How do you use the trapezoidal rule with n=5 to approximate the area between the curve #y=(3x^2+4x+2)# from 0 to 3?
Fourth, use the trapezoidal rule:
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To use the Trapezoidal Rule with ( n = 5 ) to approximate the area between the curve ( y = 3x^2 + 4x + 2 ) from ( x = 0 ) to ( x = 3 ), follow these steps:

Divide the interval ( [0, 3] ) into ( n = 5 ) equal subintervals. The width of each subinterval (( \Delta x )) will be ( \frac{3  0}{5} = 0.6 ).

Calculate the function values ( y_i ) at the endpoints and midpoint of each subinterval. For ( n = 5 ), you'll have 6 points: ( x_0 = 0, x_1 = 0.6, x_2 = 1.2, x_3 = 1.8, x_4 = 2.4, x_5 = 3.0 ).

Use the Trapezoidal Rule formula for each pair of adjacent points: [ A_i = \frac{1}{2} \cdot \Delta x \cdot (y_{i} + y_{i+1}) ] where ( A_i ) is the area of the trapezoid for the ( i^{th} ) subinterval.

Sum up the areas of all the trapezoids to get the total approximate area under the curve between ( x = 0 ) and ( x = 3 ).

The final result will be the approximation of the area between the curve and the xaxis within the specified interval using the Trapezoidal Rule with ( n = 5 ).
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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