Question

The function f(x) = 2x + 1 is defined over the interval [2, 5]. If the interval is divided into n equal parts, what is the value of the function at the right endpoint of the kth rectangle?

A) 2+3k/n
B) 4+3k/n
C) 4+6k/n
D) 5+6k/n
E) 5+3k/n

Answer 1

spread = 5-2 = 3
if cut into n pieces, each base = 3/n

endpoint of 1st rectangle = 2 + 3/n
endpoint of 2nd rectangle = 2 + 2(3/n)
...
endpoint of kth rectangle = 2 + k(3/n)

= 2 + 3k/n

f(2+3k/n)
= 2(2 + 3k/n) + 1
= 5 +6k/2

I see you have two other questions above that follow this reasoning.
Follow the same analytic thinking by setting up a pattern.

Answer 2

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