# How do you calculate the right hand and left hand riemann sum using 4 sub intervals of #f(x)= 3x# on the interval [1,5]?

See the explanation section, below.

Assuming that we are using subintervals of equal length, we get:

(Do the arithmetic.)

(Do the arithmetic.)

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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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- If the area under the curve of f(x) = 25 – x2 from x = –4 to x = 0 is estimated using four approximating rectangles and left endpoints, will the estimate be an underestimate or overestimate?
- How do you use the trapezoidal rule to approximate the Integral from 0 to 0.5 of #(1-x^2)^0.5 dx# with n=4 intervals?
- How do you find the Riemann sum for this integral using right endpoints and n=3 for the integral #int (2x^2+2x+6)dx# with a = 5 and b = 11?

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