# Rectangular Approximation (LRAM, RRAM, MRAM)

Approximate the area under a curve with the rectangular approximation method. Enter a function, f(x), change the limits x1 and x2, and then select a right-hand, left-hand, or midpoint rectangular approximation technique. Change n to adjust the number of rectangles.

Consider MRAM, RRAM, and LRAM with n=4 for the function . (You can compare them together by checking two or three of the boxes at a time) Which one do you think will give the most precise estimate? Will any of them estimate the area under this curve equally? Explain your answer.

This time change the function in the f(x) box to be "20/x". Now which RAM will overestimate the area under the curve when ? Which one will underestimate it?

Change the function in the f(x) box to be "sqrt(10x)". Now which RAM will overestimate the area under the curve? Which one will underestimate it?

Use the slider to change the value of n. As n increases, what do you observe?

What generalizations can you make about how well LRAM, RRAM, and MRAM estimate different types of curves?