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Tutorial 4

The document contains mathematical equations and limits involving functions like f(x), x^2, sinx, and logarithms. It explores concepts like continuity, derivatives, and taking limits as x approaches various values.

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keungboy26
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0% found this document useful (0 votes)
42 views3 pages

Tutorial 4

The document contains mathematical equations and limits involving functions like f(x), x^2, sinx, and logarithms. It explores concepts like continuity, derivatives, and taking limits as x approaches various values.

Uploaded by

keungboy26
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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" I degrees

7 degree

"
2

-
1Eit 130
=O

4X

t ~
,
2
= IX i it

it "
i
X

x
->

>

f(x) =

x for x >0

f -(x) =
inverse of f(x)

Sinx +

to x
-
im
anty-arctan-tank
e

-
G

↓ ↓ ↓
7 y
j
= x2
=

4 -x9 - X I
#, +
-

-
Ex
6
32
=

·
2
=

lim
·
x - 1 f(x) =

f()
limf(x) :
f (z)
8 c d
((E d) 7(2)
= +

-
+

d 14
4
=

I =>

then
it
=R

limf(x) exists
-

f(a)
a
x
=

f continuous at
If Eaf(a)=L= f(a) ,
is

xig, E -> x
-

y3
y)(x y2)
-lim
=(x xy
+

+
-

7
x
->

81
9 -

- (x))
-lin9+
9.x+
-
x 81 -

x(81 +

95x +

x)
81)
S
9x9

181
⑭or
e
=

9 +
+ +
extra

x +
0x
x
xt m
x i

W
-f(x)
/im f(x)
osloge
=

↓X-0 wx

Ix)
X *
12x/cos3x
lim f'(0)-mfca
f(x) =

12x)cos3 x
2xcos3x if x = 0

E -xcossx if x <0

aliror os(xonee -
~
--2

x Sin (sinz)

im in
Si

(x) e
e

sin(sin)] E
-
I Sin =

cos

x2
-

- (2x
*

cos(sin) in)
-

-
.
(2).( t
caus(E)
<
-

-
n

* cos(sin) cos(- )
= -2 ·

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