(b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann integrable on [1,2]. Evaluate the Riemann integral tion Pn= 1, n+1 n+2 n n n Hint: (1) Each (sub)interval is given by [n+i-1 n+i " 1 dx by using definition with the parti- n 1-1,2}, n 1≤i≤n. nEN. (2) Use the formulae Σ(n+i-1)³ = n²(15n² — 14n+3), 2(n+i)³ = n²(15n² + 14n+3). i=1
(b) (c) Explain the differentiability of f on R by using definition. 1 Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann integrable on [1,2]. Evaluate the Riemann integral tion Pn= 1, n+1 n+2 n n n Hint: (1) Each (sub)interval is given by [n+i-1 n+i " 1 dx by using definition with the parti- n 1-1,2}, n 1≤i≤n. nEN. (2) Use the formulae Σ(n+i-1)³ = n²(15n² — 14n+3), 2(n+i)³ = n²(15n² + 14n+3). i=1
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
2c
Transcribed Image Text:Let the function f: R→ R be defined by
1
x2,
f(x) =
=
0,
x=0,
x = 0.
![(a)
(b)
(c)
Explain the differentiability of f on R by using definition.
Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann
integrable on [1,2].
1
Evaluate the Riemann integral f(x) dx by using definition with the parti-
tion
2n=1,2},
Pn
={₁,
=
n+1 n+2
n
9
n
n
Hint: (1) Each (sub)interval is given by
n+i-1 n+i
nti
"
2+1].
n
1 ≤ i ≤n.
n
(2) Use the formulae
1
Σ(n+i − 1)³ = ²n² (15n² − 14n+3), (n+i) ³ = n²(15n² +14n+3).
i=1
nEN.
i=1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0cbf176c-0f96-42e6-b6a7-5c532cc62a52%2Fc4a3c7de-fbb4-44b8-b047-52266fdd4278%2Fple5xj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a)
(b)
(c)
Explain the differentiability of f on R by using definition.
Let f' be the first derivative of f computed in Q1(a). Explain why is Riemann
integrable on [1,2].
1
Evaluate the Riemann integral f(x) dx by using definition with the parti-
tion
2n=1,2},
Pn
={₁,
=
n+1 n+2
n
9
n
n
Hint: (1) Each (sub)interval is given by
n+i-1 n+i
nti
"
2+1].
n
1 ≤ i ≤n.
n
(2) Use the formulae
1
Σ(n+i − 1)³ = ²n² (15n² − 14n+3), (n+i) ³ = n²(15n² +14n+3).
i=1
nEN.
i=1
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