Calculate the following limits limx→ax3−a3x4−a4

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Calculate the following limits  limx→ax3−a3x4−a4

dieseisB · Accepted Answer

Step 1  Given   limx→ax3−a3x4−a4  We have to evaluate the limit.   Step 2  We have   limx→ax3−a3x4−a4  ⇒limx→a(x−a)(x2+xa+a2)(x2−a2)(x2+a2)   (Done factorization)  ⇒limx→a(x−a)(x2+xa+a2)(x+a)(x−a)(x2+a2)   (Again done factorization)  ⇒limx→a(x2+xa+a2)(x+a)(x2+a2)   (Cancelling out common factor)   ⇒limx→a(a2+a×a+a2)(a+a)(a2+a2)   (Substituting the limit)  ⇒limx→a(3a2)(2a)(2a2)  ⇒32×(2a)  ⇒34a  So,  limx→ax3−a3x4−a4=34a

Calculate the following limits limx→ax3−a3x4−a4

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