Please see the picture below and only answer part 2,3,4,5 3. (14pts) Show using Questions 1 and 2 that N+1(ba)2 andL(f,PN) =a(ba) (ba)2N N+1(ba)2+N2...

Please see the picture below and only answer part 2,3,4,5

3. (14pts) Show using Questions 1 and 2 that

N +1(b−a)2

and L(f,PN) = a(b−a)−

(b−a)2N

N +1(b−a)2+ N 2

U(f,PN) = a(b−a)+ NConclude that:

lim U(f,PN) =N→∞

4. (13pts) Use Question 3. to infer that given any ε > 0, there exists a partition P of[a, b] such that:

b2 a2 b2 a2

2 − 2 −ε≤L(f,P)≤U(f,P)≤ 2 − 2 +ε

5. (13pts) Use Question 4. to show that f is Riemann integrable on [a, b] and that

b b2a2

f(x)dx= 2 − 2.

• Attachment 1
• Attachment 2