Question

How to prove that this is increasing?

Answer 1

\[\frac{ 2n-3 }{ n+1 }\]

Answer 2

ok, what course are taking, precalc or calc?

Answer 3

analysis

Answer 4

One way you can do it with calculus is to take the derivative. If the expression is always increasing, then its derivative will always be more than zero.

Answer 5

ill explain it conceptually. when you say increasing I assume you mean "it increases as x increase"

Answer 6

think about it this way. if i give you a really big number and tell you to add 2 or 3 will it make much of a difference? no. but what if i told you to multiply it my 2 or 3? that would make a big difference

Answer 7

if you want some hard work to do, prove that if \(m<n\) then \[\frac{2m-3}{m+1}<\frac{2n-3}{n+1}\]

Answer 8

so lets try pluggin in a value for n. lets start with 10. so the whole thing equals 17/11. now lets try using 20. we get 37/21. now try one hundred. we get 197/101. keep going and the fraction keeps getting bigger and approaches 2. i say approaches because it will never actually get there