Question

大学高数极限连续问题

求解答谢谢

Answer 1

lim(x->-8) [√(1-x) -3 ]/[ 2+x^(1/3) ] =lim(x->-8) [(1-x) -9 ]/{ [ 2+x^(1/3) ] . [√(1-x) +3 ] } =lim(x->-8) (-8-x)/{ [ 2+x^(1/3) ] . [√(1-x) +3 ] } =(1/6) lim(x->-8) (-8-x)/ [ 2+x^(1/3) ] =-(1/6) lim(x->-8) (8+x)/ [ 2+x^(1/3) ] =-(1/6) lim(x->-8) [2+x^(1/3)]. [ 4-2x^(1/3)+ x^(2/3) ]/ [ 2+x^(1/3) ] =-(1/6) lim(x->-8) [ 4-2x^(1/3)+ x^(2/3) ] =-(1/6) [ 4 +4 +4] =-2