## anonymous 5 years ago Help me to understand this please.

1. anonymous

$e^{x}\times \sin x \times -\cos x$

2. anonymous

Here is the graph of that function. http://tinyurl.com/4cazsvl As x approaches -infinity, sin and cos simply oscillate,while e^x approaches 0, which makes the limit 0. As x approaches infinity, e^x becomes extremely large, making the function oscillate wildly.

3. anonymous

uh thanks one more thing what is the solutıon of the equation $-\cos x \times \sin x = ?$

4. anonymous

So you need to find solutions that cause sin(x) = 0 and cos(x) = 0 Sin(x) = 0 when x = pi * n Cos(x) = 0 when x = (pi/2) * n Combine the two, so every multiple of pi/2 = 0

5. anonymous

thank you so much for your reply but what i ask is exactly this =>, for ex: $e^{x}\times(-\sin x)\times(-\sin x) = e^{x}\times(\sin^{2}x)$ and what is: $e^{x}\times(\sin x)\times(-\cos x) = ?$

6. anonymous

Well your first equation is an identity. The solutions to the second equation are exactly the same as what I posted above. I'm still not 100% are you asking for the roots?

7. anonymous

yes i am asking for the roots for $- \cos x \times \sin x =$ or $-\sin x \times \cos x =$

8. anonymous

Okay then $(\pi/2)*n$ n is any integer

9. anonymous

thank you very much

10. anonymous

You're welcome

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