Answer:
The maximum error in the calculated area of the rectangle is
Step-by-step explanation:
The area of a rectangle with length and width
is
so the differential of <em>A</em> is
so
We know that each error is at most 0.1 cm, we have ,
. To find the maximum error in the calculated area of the rectangle we take
,
and
,
. This gives
Thus the maximum error in the calculated area of the rectangle is
The series of odd numbers is:
1, 3, 5, 7, 9, 11, 13, ....
If you observe this series, it is an Arithmetic Series with first term as 1 and common difference of 2. Common difference is defined as the difference between two consecutive terms of the series. So by using the formula of sum of an Arithmetic Series, we can find the sum of first 100 positive odd whole numbers.
The formula for the sum of an Arithmetic Series is:
Here,
n = number of terms = 100
a₁ = first term = 1
d = Common Difference = 2
Using the values, we get:
Thus, the sum of first 100 positive odd whole numbers is 10,000.