math assignment set 1
TRANSCRIPT
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SUBJECT:
MATHEMATICS ENGINEERING
SET 1
NAME OF LECTURER : DR.MARSYITA
GROUP :
DUE DATE : 24 NOVEMBER 2014
NAMA NO.
MATRIK
NO. KAD PENGENALAN
LIM JUN RONG 178463
KUAN POH YEE 176762 940202-08-5218
WONG SWEE YAO
LOW BEE SAN
LIM KOK SANG
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Question 1 (10 marks)
Find the following limits.
Solution
Since takes the form
at x =8, we apply L Hpitals rule to give
=2
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Using trigonometric identity,
Since
takes the form at x = , we apply L Hpitals rule to give
Question 2 (15 marks)
Sketch the graphs of the following functions IT tools for .
a)
||
b) ||c) ||
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Solution
a) || ,
b) ||
x f(x)
-2 4
-1 2
0 0
1 0
2 0
x f(x)
-2 -4
-1 -1
0 0
1 12 4
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c) ||
x f(x)-2 -1
-1 -1
0 undefined
1 1
2 1
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Question 3 (10 marks)
Two water waves,
and
, meet. Find the equation for the
resultant wave and compare its characteristics with those of the original waves. Discuss the
following special cases:
a)
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b) c)
Solution :
To find the equation for the resultant wave , sum the equation of first water wave () and secondwater wave ( .Equation for resultant wave
Let resultant wave be, +
+
+ By using the formula of trigonometric identities :
*[
Equation for resultant wave ,
Comparing the resultant wave with both the original waves.
RESULTANT WAVE ORIGINAL WAVE
Amplitude is higher than original wave. Amplitude is lower than resultant wave.
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Standing wave. Progressive wave.
a) When ( ) Since cos 0 = 1,
New original waves do not have any significant changes.
The new resultant wave
will now have a phase difference of
.
b) When ( ) ( ) Since , X = [ ] New original wave has no change but will become which
leads the old by . The new resultant wave will have a lower magnitude.
c) When
( )
( ) Since ,
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New original wave has no change but will become which
lags the old by . The new resultant wave
will become 0.
Question 4 (5 marks)
A projectile is launch from level ground at with initial velocity at an angle to thehorizontal. Subsequently, its position is described by ,
Find the equation of trajectory of the projectile. If , find where the projectile hits theground on its returns.
Solution :
y
0 x
= =
Since velocity, v =
Horizontal distance: x =) tx =
Vertical distance: Sy= t + 2
u
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Since a = -g, so y= ()t - 2Trajectory equation:
x = t =
y = () t - 2
= ( ) - 2
= y = - (1 + )
time of flight, t =
since , t
=
Position of x = )
= ( )( )
x=
Trigonometric identities:
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Question 5 (10 marks)
Express the following in partial fraction:
a)
b)
Solution :
a)
[
]
When
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By substituting and into
,
*Answer
Solution :
b )
+ When = 2 ,
+
+
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When = 3 ,
+ +
By substituting 22 and 16into ,
*Answer
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