Continuous Functions - Page 4

Questions
  • What are the the three things a continuous function can't have?
  • How many continuous functions f are there which satisfy the equation #(f(x))^2 = x^2# for all x?
  • How do you find the values of 'a' and 'b' that make f(x) continuous everywhere given #(x^2 - 4)/(x - 2)# if x < 2, #ax^2 - bx + 3# if 2 < x < 3 and #2x - a + b# if #x>=3#?
  • Verify Rolle theorem for function: f(x)= #x^3-6x^2+11x-6# in the interval [1,3] ?
  • What are the three conditions necessary for the function f(x) to be continuous at the point x = c?
  • How do I find all intersection points of #f(x)=ax^4# and #g(x)=bx^2# where a,b > 0?
  • For what value of the constants A and B is the function f(x)=8 continuous for all X if x = 5?
  • Determine where f is continuous when f(x)=(lnx)^2?
  • Judge the following is true or false If f is continuous on ( 0,1 ) then there is a c in (0,1) such that f(c) is a maximum value of f on (0,1)?
  • How do you use the definition of continuity to determine weather f is continuous at #2-x# if x<1, 1 if x=1 and #x^2# if x>1?
  • How do you use the definition of continuity to determine weather f is continuous at #f(x)= x-4# if #x<=0# and #x^2+x-4# if x>0?
  • How do you show that the function #h(x)=xe^sinx# is continuous on its domain and what is the domain?
  • How do you show that the function #g(x)=sqrt(x^2-9)/(x^2-2)# is continuous on its domain and what is the domain?
  • What is the continuity of the composite function #f(g(x))# given #f(x)=x^2# and #g(x)=x-1#?
  • What is the continuity of the composite function #f(g(x))# given #f(x)=1/sqrtx# and #g(x)=x-1#?
  • What is the continuity of the composite function #f(g(x))# given #f(x)=1/(x-6)# and #g(x)=x^2+5#?
  • What is the continuity of the composite function #f(g(x))# given #f(x)=sinx# and #g(x)=x^2#?
  • Over what domain is #f(x)=sin(x)# continuous ?
  • Is the function #x-4# continuous if 3 < x < 4?
  • What is the limit of #7/4(x-1)^2# as x approaches 1?