当x趋近于无穷大时,求下列函数极限★(sinx+cosx)/x★(2^n+1+3^n+1当x趋近于无穷大时,求下列函数极限★(sinx+cosx)/x★(2^n+1+3^n+1)/2^n+3^n★(x-cosx)/x

Question

当x趋近于无穷大时,求下列函数极限 ★(sinx+cosx)/x ★(2^n+1 +3^n+1
当x趋近于无穷大时,求下列函数极限
★(sinx+cosx)/x
★(2^n+1 +3^n+1)/2^n +3^n
★(x-cosx)/x

Answer 1

lim (sinx+cosx)/x = 0,
lim [2^(n+1)+3^(n+1)]/(2^n+3^n) 分子分母同除以 3^n,
= lim [2*(2/3)^n+3]/[(2/3)^n+1] = (2*0+3)/(0+1) = 3.
lim (x-cosx)/x = lim 1-cosx/x = 1.