Test # 4 #1 ( Total 5 pts ) Show that the function FCX ) = (1 when x is rational [ C ) - E , g ( ( ) + = ) 0when X Is irattional -J , fla) to ) is discontinous ( Everywhere , (gl() ) + 5 ) # 2 ( Total 6pts ) Show that the Function g ( x ) = ( x when x is rational when x is irattional is continous only at X = 0. on # 3 ( Total 10 pts ) prove that a Function Fix ) is continous at a point X = 6 if and only if for each Sequence { xw ) 1 700 . with lim XN = C , one has lim flaw ) = FCC ). n- 700 use this to show that the Function Tan ( 1 ) IS Discontinous at X= 0. Bonus 5 pt ) Is x = 0 a removable Finite jump, or infinite ump discontinuity of can , + ) ? It yes , justify the Answer. if No, Explain why