5.1 Integration & Anti-derivatives Area Estimate Under a Function Question #5 (Medium)
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5.1 Integration & Anti-derivatives
Area Estimate Under a Function
Question #5 (Medium): Interpreting the Limit
Strategy
This is same as Question #4 but working backwards.
Based on the limit expression:
1) Determine the interval from
2) Convert into a regular function notation without the subscript .
Sample Question
Find the functional region whose area is equal to the limit.
Solution
1) It looks like
, and since ,
fits the form of . So must be .
2)
and since , then
, which means so .
So the interval is , ie.
3) Since
, then
Therefore, the limit
represents the area under the function over the
interval (ie. .