trig and limit derivatives please help asap

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find derivative
y=(secx+tanx)(secx-tanx)

find limit
lim (xcsc2x)/(cos5x)
(as x approaches 0)

lim (x+xcosx)/(sinxcosx)
(as x approaches 0)
 
Re: trig and limit derivatives

alena said:
find derivative
y=(secx+tanx)(secx-tanx)
Click to expand...
Is this written correctly? It seems that multiplying and a quick identity will simplify the whole thing substantially?
 
it's written right... i'm just not sure what step to use to take the derivative although it might be a simple thing that i'm not seeing
 
Take tkhunny's hint: Multiply it out first.

Eliz.
 
(sec^2x -tanxsecx + tanxsecx -tan^2x
so u get sec^2x-tan^2x
so the derivative is (1/cos^2x) - (sin^2x/cos^2x)
(1-sin^2x)/ (cos^2x)
so u get cos^2x/cos^2x so that equals 1
BUT THE ANSWER IS ZERO... ???
 
Take TKHunny's hint and use a trig substitution before trying to find the derivative. Do you know any identities using tan(x) and sec(x)? There is a very important one.
 
oh ok i understand i got cos^2x/cos^2x which simplifies to 1 and then u take the derivative which is 0... thx... could u help me with the other ones?
 
alena said:
find limit
lim (xcsc2x)/(cos5x)
(as x approaches 0)
Click to expand...
This one is almost famous.

Rewrite as (x/sin(2x))*(1/cos(5x)), then (1/2)*(2x/sin(2x))*(1/cos(5x))

Now what?

I'm holding out for your response to this one before saying anything about #3. Let's see if you put it together...
 
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