Question

Asked Jun 25, 2019

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C). Find an 'n' where Midpoint Rule would guarantee estimation within 6 decimal places.

Step 1

Let's get the concepts in place, before we proceed to solve this.

For an integral I (as shown on the white board), the error E_{M} under mid point rule is as given by the expression on the whiteboard.

“h” used in the expression has been defined further.

“n” is what we have to find such that E_{M} ≤ 10^{-6}

f(x) = sin(x^{2})dx

a = 0, b = 1.5

Step 2

We now proceed to calculate the double derivative of f(x). Recall

- the chain rule of calculus
- d(sinz)/dz = cosz
- : d(x
^{n}) / dx = nx^{n-1}

Please see the white board.

Step 3

In order to get the maximum value of f''(x), we need to plot f''(x) w.r.t over x = 0 to x = 1.5.

Please see the graph on the white board.

The maximum absolu...

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