Evaluate the integral , where
, by considering D as a region of Type I and then as a region of Type II.
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Evaluate the integral , where
, by considering D as a region of Type I and then as a region of Type II.
In R we have a built-in data set "trees". A screenshot of the last four rows together with the R code to obtain it is given as follows. To get more detail about this data set you can run ?trees command on R console.
```
> tail(trees, 4)
Girth Height Volume
28 17.9 80 58.3
29 18.0 80 51.5
30 18.0 80 51.0
31 20.6 87 77.0
```
Note that all the three variables of this data set are numeric. So, assuming each row of this data set is a point in 3-dimension. Find the distances between the points corresponding to the and the
rows using the Manhattan and Chebyshev distance formula.
Evaluate the integral using beta and gamma functions.
Find the equation of a line passing through points A(0, 1, 1) and B(1, 1, 0). Also, find the coordinates of a point on this line which is at a distance of 10 units from point A opposite to the side of point B.
(2 + 3 + 5)
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If be a function defined by
,
. Show that f is Riemann integrable using both definitions. Also, verify that the results of both definition match.
If f is a function from set X to a set Y then is it possible ,
? where
and