Author Topic: urgent:trigonometric equation help and a few other questions  (Read 2528 times)

Offline lhl_anecar

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urgent:trigonometric equation help and a few other questions
« on: October 16, 2010, 06:26:18 pm »
Can someone please kindly help me solve these questions

1. state the standard identity relating cos and sin arising from Pythagoras Theorem
    sec^2(x) + cosec^2(x) = sec^2(x) x cosec^2(x)

I have no idea what the question wants.

and this question

2. ln x + ln(1-x)-2ln(1+x)

It looks so simple but i just cant seem to get it right.. help :(
 
3. 5 x (1.5)^a = 100

how do i get a?

4. find the deriavative of the following

a) y=x^5e^x + 3xlnx

b. R=(e^t+1)(t-ln t)

y=(x^5)(e^x) + 3xlnx    how do i solve this??
« Last Edit: October 21, 2010, 01:23:01 am by lhl_anecar »

Freaked12

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Re: urgent:trigonometric equation help and a few other questions
« Reply #1 on: October 16, 2010, 09:07:56 pm »
what do you have to do
 simplify ?
 or equate ?

if we simplify
its coming
 ln[ (x-x*) / (1+x)* ]
 x* means x squared

and if we equate

 then you remove the ln
 by making the other side the power of e
 and equation it to the thing iside the ln bracket
 that will make a quadratic equation in x




Freaked12

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Re: urgent:trigonometric equation help and a few other questions
« Reply #2 on: October 16, 2010, 09:18:03 pm »
just remember
if lnx - lnx
then its equal to ln [ x/x ]
and if lnx + lnx then it equals ln [x multiplied by x ]

Offline ashish

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Re: urgent:trigonometric equation help and a few other questions
« Reply #3 on: October 17, 2010, 02:36:13 am »
Can someone please kindly help me solve these questions

1. state the standard identity relating cos and sin arising from Pythagoras Theorem
    sec^2(x) + cosec^2(x) = sec^2(x) x cosec^2(x)

I have no idea what the question wants.



the equation is
cosx2 + sinx2 = 1

for the second one i have to prove ?

secx is 1/cosx  and cosecx is 1/sinx

from left hand side

sec2x + cosec2x = 1/cos2x + 1/sin2x
         expressing as a single fraction
 
                                                      =(sin2x + cos2x)/ cos2x sin2x
                                                       = 1/sin2x   *   1/cos2x

                                                        = cosec2x  *  sec2x

Offline ashish

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Re: urgent:trigonometric equation help and a few other questions
« Reply #4 on: October 17, 2010, 02:47:12 am »
Can someone please kindly help me solve these questions



It looks so simple but i just cant seem to get it right.. help :(
 
3. 5 x (1.5)^a = 100

how do i get a?



3.5 * (1.5)a =100
          1.5a= 100/3.5
         taking ln on both side
         ln1.5a= ln(100/3.5)
                  power becomes multiplier (one property of log)
                  a=(ln(100/3.5))/ln1.5
                   a =8.268

Offline ashish

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Re: urgent:trigonometric equation help and a few other questions
« Reply #5 on: October 17, 2010, 05:36:11 am »
Can someone please kindly help me solve these questions



4. find the deriavative of the following

a) y=x^5e^x + 3xlnx

b. R(e^t+1)(t-ln t)

4.a
let do it part by part

y=X5ex

dy/dx = X5ex-1 *5ex


second part using quotient rule

Udv/dx + Vdu/dx
= 3x*(1/x) + 3lnx
=3+3lnx

add these two

5exX5ex-1 + 3 + 3lnx

i just hope i didn't do any mistake with superscript 

Offline ashish

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Re: urgent:trigonometric equation help and a few other questions
« Reply #6 on: October 17, 2010, 06:08:40 am »
for 4b i think you missed something  ???

Offline lhl_anecar

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Re: urgent:trigonometric equation help and a few other questions
« Reply #7 on: October 18, 2010, 12:19:00 am »
thanks for the help!! appreciate it loads.. it's really kind of you guys to help me out.
i just have one last question that i am still unsure about and hope u guys can help me out
 which is

using the product rule to find the derivatives of the following..

a)  x^2[?x + (1/?x)]


thanks again!!

Offline lhl_anecar

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Re: urgent:trigonometric equation help and a few other questions
« Reply #8 on: October 18, 2010, 12:22:27 am »
for 4b i think you missed something  ???

R=(e^t+1)(t-lnt)  

i missed out the = sign, sorry about that,i just don't seem to get how to differentiate ln. please help. thanks!!! :)

« Last Edit: October 19, 2010, 06:56:54 am by Deadly_king »

Offline ashish

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Re: urgent:trigonometric equation help and a few other questions
« Reply #9 on: October 19, 2010, 02:34:36 am »
oops sorry hey i have to go to school for exams ,, :-\  when i will do it when i will be back or maybe someone here will do it in the mean time  ::)

Offline Deadly_king

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Re: urgent:trigonometric equation help and a few other questions
« Reply #10 on: October 19, 2010, 06:43:54 am »
thanks for the help!! appreciate it loads.. it's really kind of you guys to help me out.
i just have one last question that i am still unsure about and hope u guys can help me out
 which is

using the product rule to find the derivatives of the following..

a)  x^2[?x + (1/?x)]


thanks again!!

First you need to expand the brackets and replace square roots by power 1/2.

Let y = x2(x1/2 + 1/x1/2)

Since they all have the same base(x), multiplication implies addition of powers while division implies subtraction of powers ;)

y = x(2+1/2) + x(2-1/2) ----> y = x5/2 + x3/2

From here it's easy to differentiate : dy/dx = 5/2 x3/2 + 3/2 x1/2

The required solution can be simplifies as (5x3/2 + 3x1/2)/2

Hope it helps :)

Offline Deadly_king

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Re: urgent:trigonometric equation help and a few other questions
« Reply #11 on: October 19, 2010, 06:57:31 am »
R=(e^t+1)(t-lnt)  

i missed out the = sign, sorry about that,i just don't seem to get how to differentiate ln. please help. thanks!!! :)


Is it R = (e(t+1))(t - lnt) or R = (et + 1)(t - lnt) ???

Offline lhl_anecar

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Re: urgent:trigonometric equation help and a few other questions
« Reply #12 on: October 19, 2010, 07:54:42 am »
Is it R = (e(t+1))(t - lnt) or R = (et + 1)(t - lnt) ???

R = (et + 1)(t - lnt) it is this one..  ;D sorry about the typing error. thanks!!!
« Last Edit: October 19, 2010, 08:23:57 am by Deadly_king »

Freaked12

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Re: urgent:trigonometric equation help and a few other questions
« Reply #13 on: October 19, 2010, 08:37:13 am »
well we can use the product rule

u = e^t + 1
u' = e^t

v = t - ln t
v' = 1 - 1/t

dR/dt = u'v + uv'
= e^t (t - ln t) + (e^t +1).(1-1/t)

Tell me if this is wrong.

Offline lhl_anecar

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Re: urgent:trigonometric equation help and a few other questions
« Reply #14 on: October 21, 2010, 01:15:09 am »
y=(x^5)(e^x) + 3xlnx

how do i solve this?? i made a mistake typing the previous question... my bad, made the whole question more difficult..
someone..please help me out, again.. thanks!! thank you very very much......