c programming language: In this task, a simple implementation of the bisection method for finding roots of continuous functions is to be developed. Let $\backslash ($f: $[$a$,$ b$]\backslash$to $\backslash$mathbb$\{$R$\}\backslash )$ be a continuous function with $\backslash ($a $<$ b$\backslash )$ and $\backslash ($f$($a$)-$ f$($b$)<0\backslash ).$ According to the intermediate value theorem, $\backslash ($f$\backslash )$ has at least one root in $\backslash ([$a$,$ b$]\backslash ).$ The bisection method works as follows:$1.$ Set $\backslash ($L $=$ a$,$ R $=$ b$\backslash )\mathrm{.}2.$ If the condition $\backslash ($f$($L$)\backslash$cdot f$($R$)<0\backslash )$ is not met, terminate. Otherwise:$3.$ Test whether $\backslash ($R $-$ L $<\backslash$text$\{$TOL$\}\backslash ),$ where $\backslash (\backslash$text$\{$TOL$\}\backslash )$ is user tolerance $($e$.$g$.,\backslash (\backslash$text$\{$TOL$\}=10^\{-7\}\backslash )).$ If yes, there is a root in $\backslash ([$L$,$ R$]\backslash )$; otherwise,$4.$ Continue with subintervals $\backslash ([$L$,($L$+$R$)/2]\backslash )$ and $\backslash ([($L$+$R$)/2,$ R$]\backslash )$ following step $2.$Write a recursive function $`$void bisect$($double L$,$ double R$,$ double TOL$)`$ implementing the bisection method, and a $`$double$`$ function $`$f$($double x$)`$ returning $\backslash ($f$($x$)\backslash ).$ Test your implementation with various functions and intervals, outputting the intervals containing roots and the function values at the midpoint. For instance, running with $\backslash ($f$($x$)=13$x$^4-1\backslash )$ and $\backslash ($L $=0,$ R $=7\backslash )$ might produce output like:"A root of f lies in $[4\mathrm{.}044723$e$+00,4\mathrm{.}044723$e$+00]$ f$(($L$+$R$)/2)-2\mathrm{.}074738$e$-08.$"For $\backslash ($f$($x$)=\backslash$sin$($x$)\backslash ),$ you might get output similar to:"A root of f lies in $[0\mathrm{.}000000$e$+00,5\mathrm{.}215406$e$-08]$ f$(($L$+$R$)/2)-2\mathrm{.}607703$e$-08""$A root of f lies in $[3\mathrm{.}141593$e$+00,3\mathrm{.}141593$e$+00]$ f$(($L$+$R$)/2)=-1\mathrm{.}741103$e$-09""$A root of f lies in $[6\mathrm{.}283185$e$+00,6\mathrm{.}283185$e$+00]$ f$(($L$+$R$)/2)--2\mathrm{.}259483$e$-08."$