lim(n趋近于正无穷)[(x^3+x^2+1)/(2^x+x^3)](sinx+cosx)

Question

lim(n趋近于正无穷)[(x^3+x^2+1)/(2^x+x^3)](sinx+cosx)

Answer 1

lim(x->＋∞)时,sinx+cosx是有限值,先不计
则lim(x->＋∞),(x^3+x^2+1)/(2^x+x^3)
=lim(x->＋∞),(1+1/x+1/x^3)/(2^x/x^3+1)
=lim(x->＋∞),1/(2^x/x^3+1)
又lim(x->＋∞),(2^x/x^3)经过多次洛必达法则知其极限为＋∞
所以原极限为0