Question

f(x)=√x^2+x+1 - x ,当x趋近于+∞时,怎么求该函数的极限值?

Answer 1

f(x)=√x^2+x+1 - x

=(√x^2+x+1 - x)(√x^2+x+1 + x)/(√x^2+x+1 + x)

=(x^2+x+1-x^2)/x(√1+1/x+1/x^2 + 1)

=(x+1)/x(√1+1/x+1/x^2 + 1)

=x(1+1/x)/x(√1+1/x+1/x^2 + 1)

=(1+1/x)/(√1+1/x+1/x^2 + 1)

limx->+∞f(x)=1/(√1+0+0 +1)

=1/2