Continuous Functions - Page 5

Questions
  • How to prove that #f(x)=|x|# is continue at #0# ?
  • Find the values of m and b that make f continuous everywhere: m = ? b = ?
  • Which values of x this function is continuous? (x non-negative real number and n->infinity)
  • Show that f(x)=2a+3b is continous, where a and b are constants?
  • How do you prove that the function: #T(x) = 1 / (abs(x-2)-x^2)# is continuous between [1.5,8]?
  • Is the function #2-x# continuous if 2 < x ≤ 3?
  • Is a function differentiable at all points that it is continuous?
  • If g(x)=x if x<0, x^2 if #0<= x <=1#, x^3 if x>1, how do you show that g is continuous on (all real #'s)?
  • What is #lim x->2^(+)# of #3/(x-2)#?
  • Let #f# be a continuous function on the closed interval #[-3,6]#. If #f (-3)=-1# and #f (6)=3#, what does the Intermediate Value Theorem guarantee?
  • What value of #a# would make the function #h(x)={x^3+a^3# if #x<2# and #4-2x# if #x>=2# continuous?
  • What are the critical values, if any, of #f(x)=e^x#?
  • For what values of #x# is the function #f(x)=ln((x-1)/(x+2))# continuous?
  • How do you prove that the limit #f(x)= x^2 + 2x - 5 =3# as x approaches 2 using the formal definition of a limit?
  • is there a function f from the reals to the reals which is not continuous,but has a continous square?
  • We have #f:RR->RR,f(x)=|x|root(3)(1-x^2)#.Is this function continous in #x=0#?
  • How do you find #\lim _ { x \rightarrow 2^ { - } } \frac { f ( x ) - f ( 2) } { x - 2}#?
  • What would be an example of a function f defined for all real numbers which has the property that lim to +1 and lim to -1 are both equal to - infinity?
  • Examine continuity of function f(x) =( (e^1/x)-1))/((e^1/x)+1)) at x=0 ?
  • F(x)= ax+3 ; #0≤x<1/2# f(x)= #sqrt((2x-1)/(x+15))# ; #1/2≤x≤1# f(x)= #(sqrt(x+3)-2)#/(x-1) ; #x>1# Find the value of a that makes f(x) continuous in #1/2# ?