# Continuous Functions - Page 6

Questions

- Is f(x)=1/(x-5) continuous at x=5?
- Prove that x^n is continuous at x=n, where n is positive integer?
- On an interval #[a,b]#, #f# is a continuous function. If #f(a)<0# and #f(b)>0#, then there exists a constant #c\in [a,b]# such that #f(c)=0# by which theorem?
- Determine whether Rolle's Theorem can be applied to #f# on the closed interval #[a,b]#. If Rolle's Theorem can be applied, find all the values of #c# in the open interval #[a,b]# such that #f^'(c)=0#?
- The function #f# is defined by #f(x)=(x-1)(3+x)#, #x>b-1# #f(x)=-x+1#, #x<=b-1# and is continuous at #b-1#. What is #b#?
- Is the function #y = x^3 + 12x^2 - 39x + 57# discontinuous at any value of #x#?
- Determine the value of the constant ''a'' for wich the funcion is continuous at x==-5 f={(x^2+6x+5)/x+5 if x not equal -5 a if x = -5 ?
- On what interval is the function f (x) = x^3 e^x increasing?
- Why is #y=1/x# a continuous function?
- How to test continuty of this function ? f(x) = #(1+x)^(1+x)# x is not equal zero
- Is there a empty function? it means that there is no line on the graph
- Solve the functional equation #f(x_1+x_2) = f(x_1)f(x_2)# ?
- For what value of L the function is continuous?
- A function f(x), a point ( x)0, the limit of f(x) as x approaches (x)0, and a positive number ε is given. Find? a number such that for all x, 0 < < δ ⇒ < ε f(x) =6(x) - 9, L = -3,(x)0 = 1, and ε = 0.01
- How to prove that #f# is continuous?
- Choose the value of k that makes the following function continuous at x=1: Help!?
- What value of k makes the following function continuous?
- In a limit, what is the difference between #lim_(x->a)#, #lim_(x->a^-)#, #lim_(x->a^+)# where #ainRR#?
- How is the function #1/9*x^3 +5, x<-3# not continuous at x=1 and what type of correspondence does it display?
- F(x)=(e^1/x +1)/(e^1/x -1) is function continuous at x=0?