This problem studies a new rational function: t$($x$)=(7$x$^4-101$x$^3+540$x$^2-1204$x $+958)/($x$^4-14$x$^3+72$x$^2-151$x $+112)($a$)$ Plot t$($x$),$ evaluated via Horner$$s rule, along with the following $($equivalent$)$ continued fraction, from x $=0$ to x $=4$: u$($x$)=7-3/($x$-2-1/($x$+7+10/($x$-2-2/($x$-3))))$ You may wish to know that:

u$(1)=10,$ u$(2)=7,$ u$(3)=4\mathrm{.}6,$ u$(4)=5\mathrm{.}5($b$)$ Evaluate each of these functions for x $=10^(77)($make sure to use floats in your code$).$

Do you understand what is happening? Are you starting to prefer one formulation

over the other? $($What happens if you use integers instead of floats?$)$

$($c$)$ Plot the two Python functions $($t$($x$)$ and u$($x$))$ for x $=2\mathrm{.}400+2^(52)$ i$,$ where i goes

from $0$ to $800.$ Was your intuition $($about which formulation is better$)$ correct?