Prove that there exists a real number x such that x^177+165/(1+x^8+sin^2(x))=125 using Intermediate Value Theorem.

Josiah Owens 2022-10-26 Answered
Prove that there exists a real number x such that x 177 + 165 1 + x 8 + sin 2 ( x ) = 125 using Intermediate Value Theorem.
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Answers (1)

Remington Wells
Answered 2022-10-27 Author has 13 answers
Define
f ( x ) = x 177 + 165 1 + x 8 + sin 2 ( x ) 125.
Clearly f ( x ) is continuous in [ 2 , 2 ]. Since f ( 2 ) < 0 , f ( 2 ) > 0, there is c ( 2 , 2 ) such that f ( c ) = 0.
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