How do you use the trapezoidal rule with n=4 to approximate the area between the curve # sin (x^2)# from 0 to 1/2?
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To use the trapezoidal rule with n=4 to approximate the area between the curve sin(x^2) from 0 to 1/2, follow these steps:

Divide the interval [0, 1/2] into n equal subintervals. Since n=4, each subinterval has a width of (1/2)/4 = 1/8.

Determine the function values at the endpoints of each subinterval. In this case, evaluate sin(x^2) at x=0, x=1/8, x=2/8, x=3/8, and x=1/2.

Apply the trapezoidal rule formula for each subinterval. The formula for the area of a trapezoid is: Area = (1/2) * (base1 + base2) * height. The bases are the function values at the endpoints of each subinterval, and the height is the width of the subinterval.

Sum up the areas of all the trapezoids to get the approximation of the total area under the curve between 0 and 1/2.
By following these steps, you can approximate the area between the curve sin(x^2) from 0 to 1/2 using the trapezoidal rule with n=4.
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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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