• Wrong document? Swap it for free
  • Written by students who passed
  • Immediately available after payment
  • Read online or as PDF
  • 4.6 TrustPilot
0
Sell
Where do you study
Your language
Start selling Create your account
  • University Of Southampton (UOS)
  • Mathematics for Engineering and the Environment (MATH1054)
To add items to your wishlist, you must be logged in
Document preview thumbnail
Preview 4 out of 133 pages
Other

MATH1054 Worksheets with Solutions

0.0
(0 reviews)
- sold
133 pages
2022/2023 Written for academic year
Institution
University Of Southampton (UOS)
Course
Mathematics for Engineering and the Environment (MATH1054)
Document preview thumbnail
Preview 4 out of 133 pages

This is a set of practice questions taken from textbooks and smaller tests with my worked solutions and notes to help understand and remember why certain errors cannot be made.

Content preview

,8 3 8
. . Exercise du = 4x3 + 2x2 + 4x2 + 2x + 2x + 1

dx = 4x3 + 6x2 + 4x + 1




v = (x3 + 2x2 + 1)4
y = 29 2 = 5x + 3 W = x3 + 2x2 + 1 V = 04

928 d &w 3x2 4x dr 40
dy
= = = + =

di di dw

dr = dr x dw
di dw dx
dy dy x
=



= 4(23 + 2x2 + 1)3(3x2 + 4x) -
= 928x5
=
4528 =
45(5x + 38/ ndv + vdu
&x di

= (x2 + x + 1)24(x3 + 2x2 + 1)3(3x2 + 4x)
+ (x3 +1)4 2x2 +
20 - z 4x3 2x +
1 (2x2 + 2x + 1)(2x + 1)
Y = = -




625 1 (x2 1)24(23 2x2 + 1)3(3x2 + 4x)
dy d
= = + x + +
=


+ (x3 + 2x2 + 1)4
=
62 (12x2 2) - = 1225(6x2- 1) - 2(x2 + x + 1)(2x + 1)
=
(x2 +x+ 1)2(x3 + 2x2 1)3(12x2 16x)
+ + +


1)+ 2(x2 + x + 1)(2x + 1)
dy =dy the
Xd (n3 + 2x2+



=
12 (4x3 -
2x + 1)(6x 2
- 1)



*

u = (x2 + x + 1)

=duxd
u = z2 - 2 = x2 + x + 1 -


=
2 dz = 2x + 1

dx

z(x2 + 1)(2x + 1) -
dr en =
x +


2x + 1)(2x + 1)
-
= (2x2 +

, 2(4 + x2)i v = (4 + x2)
u = x
w = 4+ x2 v =wi
=w
ar
du =
dw = 2x

dr
did


dr =drX
dr =
tw e



=
-
w x


(4 + x2) Ex
-




=



I R


(4 + x2

u dv + vdu
dx di


=
x R + (4 + x2)
(4 + x2
= x2 (4 + x2 xJ4+ 22
+




(4 + x2 1 J
= x2 + (4 + x2)
(4 + x2

= 4+ 2x2 = z(z + x2)
14 + x2 (4 + x2

, (x2 + 1)
z = x3 + 1


n =
25

du = 17 dz = 2x

d2 3 dx

dy = duxdz


on
de (2)

= 25
3

1)
2(x2
=
+




192
= 24

3(x2+ 1) - 3 3 + 12




↳ Expand
2)(j)
into x + 1
+
R




1
= x
+
+ 2



2
f'(x)
-



= 1 -
1x

=
1-1
x

Document information

Study
Unknown
Uploaded on
April 12, 2025
Number of pages
133
Written in
2022/2023
Type
Other
Person
Unknown
Report Copyright Violation
$18.16
Wrong document? Swap it for free Within 14 days of purchase and before downloading, you can choose a different document. You can simply spend the amount again.
Written by students who passed
Immediately available after payment
Read online or as PDF
Seller avatar
vanessarudd
Sold
1
Followers
2
Items
5
Last sold
1 month ago

Browse related subjects

Subjects

  • mathematics
  • first year
  • engineering
  • mechanical
  • complex numbers
  • differentiation
  • integration
  • statistics
  • euler method
  • matrices
  • worksheet
  • practice questions
  • fully worked solutions

Why students choose Stuvia

Created by fellow students, verified by reviews

Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.

Didn't get what you expected? Choose another document

No worries! You can instantly pick a different document that better fits what you're looking for.

Pay as you like, start learning right away

No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.

Student with book image

“Bought, downloaded, and aced it. It really can be that simple.”

Alisha Student

Working on your references?

Create accurate citations in APA, MLA and Harvard with our free citation generator.

Learn more Create citation
Working on your references?

Frequently asked questions