In the limit
we're interested in the value that converges to as
gets closer to
. So in fact
.
In the given example, is factorized to reveal a common factor of
in the numerator and denominator. We have
if
, so
so we can simplify
and *remove* the discontinuity.
Then
The correct question is contained in the first attached file.
Answer:
a) The trapezoidal rule answer
0.433490
b) The midpoint rule answer
1.186075
c) The Simpson's rule answer
1.106143
Step-by-step explanation:
These numerical methods are means of estimating definite integrals by finding the area under the curve of the function between two points.
a) The solution for the trapezoidal rule method is presented in the 2nd attached image to this solution.
b) The solution for the midpoint rule method is presented in the 3rd attached image to this solution.
c) The solution for the Simpson's rule method is presented in the 4th attached image to this solution.
