Calculate the following limits using the factorization formula x^{n}-a^{n

Isa Trevino

Isa Trevino

Answered question

2021-10-22

Calculate the following limits using the factorization formula
xnan=1xa21xn1+axn2+a2xn3++an2x+an12, where n is a positive integer a is a real number.
limxax5a2xa

Answer & Explanation

delilnaT

delilnaT

Skilled2021-10-23Added 94 answers

Step 1
Given: limxax5a2xa
Step 2
Explanation:
limxax5a2xa=limxa(xa)(x51+ax52+a2x53+a3x54+a4x55)(xa)
=limxa(x4+ax3+a2x2+a3x+a4)
=a4+a(a)3+a2(a)2+a3(a)+a4
=a4+a4+a4+a4+a4
=5a4
Hence, limxax5a5xa=5a4
Step 3
Answer: limxax5a5xa=5a4

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