Trig Q Watch

This discussion is closed.
manps
Badges: 0
Rep:
?
#1
Report Thread starter 14 years ago
#1
Hi, I really need help with these questions.
1. Find the Fundamental period of the following periodic function

-7 cos(6 pi x )

2. A rational function is a quotient of two polynomials. Evaluate the following limit of a rational function

..lim.. -5x^9 -x^7 -8x^5 -x^4 -8x^3 -5x^2
x-->∞ 7x^7 +7x^6 +2x^5 + 2x^4 + 9x + 8
Thanks
0
shift3
Badges: 0
#2
Report 14 years ago
#2
For the second one, divide the nominator by the denominator. You'll probably get something like A + B/C, and B/C will probably tend to 0 as x tends to infinity, so the whole function will tend to what A tends to.
0
JamesF
Badges: 1
Rep:
?
#3
Report 14 years ago
#3
For the second, the numerator has order 9, the denominator has order 7, so the limit will tend to -infinity.
0
shift3
Badges: 0
#4
Report 14 years ago
#4
(Original post by JamesF)
For the second, the numerator has order 9, the denominator has order 7, so the limit will tend to -infinity.
Yeah, that's what I wanted to say, but decided to give some explanation.
0
JamesF
Badges: 1
Rep:
?
#5
Report 14 years ago
#5
(Original post by shift3)
Yeah, that's what I wanted to say, but decided to give some explanation.
Oh, sorry.

For the first, cos(x) has period 2pi, cos(ax) has period 2pi/a, so your function will have period, 2pi/6pi = 1/3.

Alternatively, for what value of a does cos(6pi(x+a)) = cos(6*pi*x)? Expanding the left,
cos(6*pi*x)cos(6*pi*a) - sin(6*pi*x)sin(6*pi*a) = cos(6*pi*x), so sin(6*pi*a) = 0 and cos(6*pi*a) = 1, hence 6*pi*a = 2pi => a = 1/3
0
X
new posts
Latest
My Feed

See more of what you like on
The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

Personalise

University open days

  • University of the Arts London
    MA Performance Design and Practice Open Day Postgraduate
    Thu, 24 Jan '19
  • Brunel University London
    Undergraduate Experience Days Undergraduate
    Sat, 26 Jan '19
  • SOAS University of London
    Postgraduate Open Day Postgraduate
    Sat, 26 Jan '19

Are you chained to your phone?

Yes (75)
19.53%
Yes, but I'm trying to cut back (155)
40.36%
Nope, not that interesting (154)
40.1%

Watched Threads

View All