Limit as x approaches infinity, involves sinx and cosx

[rygza]

y=1/2(sinx-cosx+e(^pi-x))

question: if x approaches infinity, which term or terms will dominate?
from my understanding, sinx and cosx will oscillate and the e term will approach zero. so would the answer be sinx-cosx?

please and ty

 

[ptolema]

since the e^(pi-x) term approaches 0, it has no real impact on the sin x and cos x terms. the oscillating terms mean that the limit DNE, not that the limit is sin x-cos x (answer should not be in terms of x, anyway)