Question

Help me to understand this please.

Answer 1

\[e^{x}\times \sin x \times -\cos x\]

Answer 2

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.

Answer 3

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

Answer 4

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

Answer 5

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:
\[e^{x}\times(\sin x)\times(-\cos x) = ?\]

Answer 6

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?

Answer 7

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

Answer 8

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

Answer 9

thank you very much

Answer 10

You're welcome