`lim_(x->oo)(x^4sin(1/x)+x^3)/(1+|x|^3)` – InterviewSolution

InterviewSolution

1.	`lim_(x->oo)(x^4sin(1/x)+x^3)/(1+\|x\|^3)`
Answer» `x>0 , \|x\| = x` `(x^4 sin(1/x) + x^3)/(1 + x^3)` `= (x^3{xsin(1/x) + 1})/(1+x^3)` `= (sin(1/x)/(1/x) + 1)/(1 + (1/x)^3)` `lim_(x->oo) (sin(1/x)/(1/x) + 1)/(1+(1/x)^3)` `lim_(y->0) {((siny)/y +1)/(1+y^3)}` `= (1+1)/(1+0)` `=2` Answer

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