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Limits and differentiation
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  • Course
  • Engineering Mathematics 1 (MTM511S)
  • Institution
  • Namibia University Of Science And Technology

This book of digital notes provides a comprehensive guide to the fundamental concepts of limits and differentiation in calculus. Designed for students and enthusiasts alike, the notes are structured to facilitate a deep understanding of these essential topics. Contents 1. Introduction to Lim...

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Document information

  • May 23, 2024
  • 71
  • 2023/2024
  • Class notes
  • Lutopu khoa
  • Mainly differentiation and limits chapter

Subjects

  • differentiation
  • math
  • limits
  • engineering

Written for

  • Namibia University Of Science And Technology
  • Engineering Mathematics 1 (MTM511S)
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, Limits
·
state and work with definition of limit

·
Demonstrate , describe and recognize ways
in which limits do not exist

· calculate derivatives of functions (10 calc)

· Write and explain the definition of absoulte
masc and min of a function .




Def : the behaviour of a function as the
independent variable a certain
approaches value .

Lo

f(x) = x + 1 as "x"approaches "1"
x

1. &
,
1 80
.

,
1 .
594/1/ 1 000
,

,
1 , 001

,Note
:


·
Lim-fas : meany Limit a -c from left


himt fas ! limit + right
·
means from


· Lim - f(x)
, " means limit a -
from both


if n and k are constant then :

① Limock = k
② Limocx = C




O
3 Limo-cx = ch ④ Limoc 1fca) =
n time fa)


O
S Limo (fog(s]
=
Limayfe Lima (g(x)


2 .

98

a) Lim + 26 = or


b Lim +23x2 = 312 = 122
c)
Limx
3x + 4 =
3(1) + 4
= 0 . 88h
+
15x + 7
3(1) +7


↓) Lima1-Ecs where ~x-252, if <
2x else


( -
2)2 =
1

, # Limits in the form of (8)
can be found by either :

① dividing certain factors and
out
getting rid ofdenomi
② ration lize the numerator or denominator

③ use formula L'hospitals rule :
f (x)
Ling =
Linc , y x




2 .

g8
2 4
x
-




6) Lim z x -
2



(x -
2)(x + 2)

(x -

2)

-
x +2

=
4
x2 -
&
b) Lim
* -3 x2 +
35


(x
-

3)(x+ 3)

x(x + 3)

3 3
x 3
-
-
-




=

x -
3
= 2

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