Question

极限计算 2n-3n/2n+1+3n+1 n趋于正无穷大 (n n＋1为次方) x-sinx/x+sinx x趋于正无穷

Answer 1

1.

lim (2^n-3^n)/(2^(n+1)+3^(n+1))

上下同除3^n

=lim ((2/3)^n-1)/(2*(2/3)^n+3)

=(0-1)/(0+3)

=-1/3

2.

lim (x-sinx)/(x+sinx)

上下同除x

=lim (1-sinx/x)/(1+sinx/x)

=(1-0)/(1+0)

=1

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