By using the Intermediate value theorem.Show that f is continuos on [ − 1 ,...

gorgeousgen9487

gorgeousgen9487

Answered

2022-07-08

By using the Intermediate value theorem.

Show that f is continuos on [ 1 , 1 ], then there exist n in the natural numbers such that the equation f ( x ) + n = n ( e x ) has a solution in [ 1 , 1 ].

I'm having trouble solving this problem. Any help is appreciated.

Answer & Explanation

kawiarkahh

kawiarkahh

Expert

2022-07-09Added 15 answers

Define g ( x ) := f ( x ) + n n ( e x ). Then g is continuous and we have g ( 1 ) = f ( 1 ) + n n e and g ( 1 ) = f ( 1 ) + n n e. Can you finish it from here?

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