Calculate the following limits using the factorization formula xn−an=1x−a21xn−1+axn−2+a2xn−3+…+an−2x+an−12, where n is a positive integer a is a real number. limx→ax5−a2x−a

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Calculate the following limits using the factorization formula  xn−an=1x−a21xn−1+axn−2+a2xn−3+…+an−2x+an−12, where n is a positive integer a is a real number.  limx→ax5−a2x−a

delilnaT · Accepted Answer

Step 1  Given: limx→ax5−a2x−a  Step 2  Explanation:  limx→ax5−a2x−a=limx→a(x−a)(x5−1+ax5−2+a2x5−3+a3x5−4+a4x5−5)(x−a)  =limx→a(x4+ax3+a2x2+a3x+a4)  =a4+a(a)3+a2(a)2+a3(a)+a4  =a4+a4+a4+a4+a4  =5a4  Hence, limx→ax5−a5x−a=5a4  Step 3  Answer: limx→ax5−a5x−a=5a4

Calculate the following limits using the factorization formula xn−an=1x−a21xn−1+axn−2+a2xn−3+…+an−2x+an−12, where n is a positive integer...

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