# Definition of Continuity at a Point - Page 2

Questions

- What makes a function continuous at a point?
- How do you prove that #h(x) = sqrt(2x - 3)# is continuous as x=2?
- How do you prove that the function #xsin(1/x)# is continuous at x=0?
- How do you prove that the function #f(x) = sqrt(x) # is continuous at 0 to infinity?
- How do you find the continuity of a function on a closed interval?
- The function #f(x) = [x^2 + x] / [x]# is defined and continuous for all x except x = 0. What value of x must be assigned to f(x) for x = 0 in order that the function be continuous at x = 0?
- How do you prove that the function #f(x) = x^(1/2)# is continuous at x=1/2?
- The graph of h(x) is shown. The graph appears to be continuous at , where the definition changes. Show that h is in fact continuous at by finding the left and right limits and showing that the definition of continuity is met?
- How do you prove that the function #x*(x-2)/(x-2)# is not continuous at x=2?
- How do you prove that the function f(x) = | x | is continuous at x=0, but not differentiable at x=0?
- How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at x=-1?
- Is #f(x)=(x^2-9)/(x-3)# continuous at #x=3#?
- What is continuity at a point?
- How do you prove that the function #x*(x-2)/(x-2)# is not continuous at x=2?
- How do you find the points of continuity for #f(x)=(x-4)/(x^2-16)#?
- How do you use the definition of continuity and the properties of limits to show that the function #g(x) = sqrt(-x^2 + 8*x - 15)# is continuous on the interval [3,5]?
- How do you use the definition of continuous to prove that f is continuous at 2 given #f(x) = x^2 -3x +5#?
- What is the continuity of #f(t) = 3 - sqrt(9-t^2)#?
- How do you prove that the function #f(x) = (x + 2x^3)^4# is continuous at a =-1?
- What is the definition of inflection point? Or is it just not standarized like #0 in NN#?