solve and show work for problems please

For each problem below, determine if the piecewise function is continuous at the indicated value. Justify your answer. 1 t_' 2' x 2 2 5. x 3 __ + , x 3 Atable containin selected values off it and f' x is iven below. The function f x is continuous eve here exce tat the lacesindicated in the table. The re h of x is rovided below as well. girl 7. Find lim M. Show the work that leads to your answer. x46 x} 8. Can it be shown that there is a value c such that t) = 1 oh the interval [1, 4]? Justify your answer. 9. Can it be shown that there is a value c such that f(cl = 3 on the interval [1,4]? Justify your answer. 10. Can it be shown that there is an interval where fix) crosses the x axis? Justify your