Question

Hi guys, I am trying to find the derivative using l'Hospital's Rule.

The problem is: lim x-> pi/2 ==> (1-sin)/(1+cos(2x))

The answer is: 1/4

My trig skills aren't very good. Can someone help me answer this?

Answer 1

Basically with L'Hopital's rule you use the derivative of the function to find the limit (that's not a very good defn actually but it is essentially what you are doing)

For this question you want\[\lim_{x \rightarrow \frac{ \pi }{ 2 }} \frac{ 1-\sin(x) }{ 1+\cos(2x) }\]
if you take the derivative, you get:
\[\lim_{x \rightarrow \frac{ \pi }{ 2 }}\frac{ 1 }{ 4\sin(x) }\]
If you factor out the constants, as x approaches pi/2, sin(x) tends to 1

So the whole limit will tend to 1/4

Does that make sense?

Answer 2

can u tell me how you got 4sin(x)

Answer 3

because i understand that cos(2x) = -2*sin(2x) right?

Answer 4

Well, just take the derivaitve of it. It's a chain rule that would giveyou -2sin(2x)

Answer 5

omg