Answered

As the value of x increases, which of the following functions would eventually exceed to the other three?

1) f(x)=1000x
2) f(x)=100x²
3) f(x)=50x³
2) f(x)=2^x

Verified Answer :

kate200468

\(x\ \ \ \ \ \ \ \ |\ \ \ \ \ 0\ \ \ \ |\ \ \ \ \ 1\ \ \ \ \ \ |\ \ \ \ \ 10 \ \ \ \ \ |\ \ \ \ \ \ 100\ \ \ \ \ \ |\\-----------------------\\1000x\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ 1000\ \ \ | \ \ \ 10000 \ \ \ |\ \ \ \ 100000\ \ \ \ |\\-----------------------\\100x^2\ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ 100\ \ \ \ | \ \ \ 10000 \ \ \ |\ \ 1000000\ \ \ \ |\\-----------------------\\50x^3\ \ \ |\ \ \ \ 0\ \ \ \ \ |\ \ \ \ \ 50\ \ \ \ \ | \ \ \ 50000 \ \ \ |\ \ 50000000\ \ \ |\\-----------------------\)
\(2^x\ \ \ \ \ \ |\ \ \ \ 1\ \ \ \ \ |\ \ \ \ \ \ 2\ \ \ \ \ \ | \ \ \ \ 1024 \ \ \ |\ \ \ \ 1024^{10}\ \ \ \ \ |\\\)

\(if\ x\ \rightarrow\ +\infty\ \ \ then\)

\(f_1(x)\ <\ f_2(x)\ \ \ and\ \ \ f_1(x)\ <\ f_3(x)\ \ \ and\ \ \ f_1(x)\ <\ f_4(x)\\\\Ans.\ f_1(x)\ =1000x\)

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