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

Answer:

5+k.

Step-by-step explanation:

As you can see in the image I made the example with n=6. In general, if the interval is divided into n equal parts we have that te right value of x in the kth rectangle (Rk) is

Rk = 2+ (1/2)k

So, f(Rk) = f(2+(1/2)k) = 2(2+(1/2)k)+1 = 4+k+1 = 5+k.

Answer 2

By "f(x = 2x + 1" you likely meant "f(x) = 2x + 1."

The given interval is [2,5], and so the width of each interval is (5-2)/n, or (3/n). Since we are using right end points, the x value at the right endpoint of the kth rectangle is 2+k(3/n).  Examples:  if k=1, the value at the right endpoint is 2+1(3/n); if k=2, 2+2(3/n), and so on.  If k=n, then the value at the right endpoint is 2+n(3/n), or 2+3=5, which agrees with the given interval [2,5].

Once again, the given function is f(x) = 2x + 1.
At x = 2+k(3/n), the value of the function is 2[2+k(3/n)] + 1 (Answer).  Check:  If k=n, x = 2 + n(3/n) = 2+3 + 5, and f(5)=2(5) + 1 = 11.