How Do You Calculate Subinterval Lengths and Evaluate Functions at Endpoints?

[annoymage]

Homework Statement

suppose f(x) = x² and let I = [0,2]

i) if partition I is subdivided into n subintervals of equal length, write down the length of each subinterval,$$\Delta$$x

ii) if c_i , is the left endpoint of subinterval i, find c_i . hence find f(c_i)$$\Delta$$x

Homework Equations

N/A

The Attempt at a Solution

i) length of subintervals, T_a = ($$\frac{2a}{n^2}$$)² , a=1,2,..,n

ii) i don't understand what the question want, left endpoint of subinterval i, what actually "subinterval i"?? owho help I am not really god in english

 

[Mark44]

Homework Statement

suppose f(x) = x² and let I = [0,2]

i) if partition I is subdivided into n subintervals of equal length, write down the length of each subinterval,$$\Delta$$x

ii) if c_i , is the left endpoint of subinterval i, find c_i . hence find f(c_i)$$\Delta$$x

Homework Equations

N/A

The Attempt at a Solution

i) length of subintervals, T_a = ($$\frac{2a}{n^2}$$)² , a=1,2,..,n

The interval I is [0, 2]. Its length is 2. If you divide this interval into n smaller pieces (subintervals), each of the same length, how long is each one of the subintervals?

For example, if there are 10 subintervals, each would be 2/10 = 0.2 units in length.

ii) i don't understand what the question want, left endpoint of subinterval i, what actually "subinterval i"?? owho help I am not really god in english

If you know how long each subinterval is you can identify the left and right endpoint of each subinterval. Using my example, if n = 10, the subintervals are [0. 0.2], [0.2, 0,4], and so forth up to the last one, [1.8, 2.0].

You need to work this out more generally, using n subintervals, not a constant number like I used.

 

[annoymage]

The interval I is [0, 2]. Its length is 2. If you divide this interval into n smaller pieces (subintervals), each of the same length, how long is each one of the subintervals?

owh i thought its the length of y, ngahaha, i really need to improve my english,
if in that case, each length delta x = 2/n

For example, if there are 10 subintervals, each would be 2/10 = 0.2 units in length.
If you know how long each subinterval is you can identify the left and right endpoint of each subinterval. Using my example, if n = 10, the subintervals are [0. 0.2], [0.2, 0,4], and so forth up to the last one, [1.8, 2.0].

You need to work this out more generally, using n subintervals, not a constant number like I used.

i see i see, then ci should be

ci = 2i/n , i = 0,1,2,...,(n-1)

right?

 

[Mark44]

This will give you the left endpoints of the subintervals, yes.