$(3$pts$)$ Figure $2$ shows a function for calculating factorial number. Please analyze Big$-$O

and Big$-$Theta time complexity of the function. Please provide details.

$(3$pts$)$ Figure $3$ shows a function that uses binary search to find $($i$.$e$.$ calculate$){|}_{{?}_{?}}\sqrt[\phantom{2}]{x}{?}_{{?}_{?}}|,$

where $x$ is a natural number. Analyze the Big$-$O and Big$-$Theta time complexity of

the function. Please provide details.