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?

Answer 1

A) 2+3k/n

Explanation:

I just took the test and got an 100% so you gotta trust me on this

Answer 2

D. 5 +6k/n

Explanation:

The width of the interval is (5 -2) = 3. The width of one of n parts of it will be ...

3/n

Then the difference between the left end point of the interval and the value of x at the right end of the k-th rectangle will be ...

k·(3/n) = 3k/n

So, the value of x at that point is that difference added to the interval's left end:

2 + 3k/n

The value of the function for this value of x is ...

f(2 +3k/n) = 2(2 +3k/n) +1 = (4 +6k/n) +1

= 5 +6k/n