hi everyone,(adsbygoogle = window.adsbygoogle || []).push({});

i have to solve the problem below:

1) which is the bigger number, (without using a calculator)

B= (0.9999995)^2 / 0.9999998 & A=1.0000004/(1.0000006)^2

Then, compare those two functions on the intervall of [0;1/10] (without using a calculator)

f(x)=(1-5x)² / 1-2x & g(x)=1+4x / (1+6x)²

so, first of all, i noticed that if u put 10^-7 on f(x) you'll have the number A, and if you put 10^-7 on g(x) you'll get the number B

therefore we'll have to compare the two functions to see which is bigger, A or B. But i dun know how i am gonna compare them (do not use a calculator!!)

i tought about subsituing f(x) from g(x), here is what i got:

f(x)-g(x) <=> 51x²+60x^3+900x^4 / 1+10x+12x²+72x^3

so i have to see if this is bigger/smaller than 0.

ummm, i am not sure, but we have 0<x<1/10

so 0<51x²<51/100 & 0<60x^3<3/50 & 0<900x^4<9/100

therefore 0<51x²+60x^3+900x^4<63/100

and for the denominator we have

0<10x<1 & 0<12x²<3/25 & 0<72x^3<9

therefore 0<1+10x+12x²+72x^3<278/25

and finally, a positive number over a positive number is a positive number

so f(x)>g(x) <=> A>B (because f(x) and g(x) are increasin over [0;1/10] << I think :s )

so, is all this right ?! :uhh:

thanks for ur help :)

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# Homework Help: A function's question

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