Definition of Continuity at a Point

Topic Page

Questions

• What are the three conditions for continuity at a point?
• What is continuity at a point?
• What is the definition of continuity at a point?
• What does continuous at a point mean?
• What makes a function continuous at a point?
• How do you find the points of continuity and the points of discontinuity for a function?
• What does continuity mean?
• How do you use continuity to evaluate the limit #arctan(x^2-4)/(3x^2-6x)#?
• How do you find the points of continuity of a function?
• How do you find the continuity of a function on a closed interval?
• If #f(x)= (x^2-9)/(x+3)# is continuous at #x= -3#, then what is #f(-3)#?
• How do you find the points of continuity for #f(x)=(x-4)/(x^2-16)#?
• How do you prove that the function #x*(x-2)/(x-2)# is not continuous at x=2?
• For what intervals is #f(x) = tan((pix)/4)# continuous?
• What is the continuity of #f(t) = 3 - sqrt(9-t^2)#?
• 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#?
• 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?
• Why is #f(x)=sqrtx# continuous?
• How do you find where #f(x)=1/ln(x)# is continuous and differentiable on which interval(s)?
• How do you prove that #g(x) = 1/2x# is continuous at #x=1/4#?
• How do you prove that #h(x) = sqrt(2x - 3)# is continuous as x=2?
• 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 + 2x^3)^4# is continuous at x=-1?
• How do you prove that the function #f(x) = sqrt(x) # is continuous at 0 to infinity?
• How do you prove that the function #f(x) = x^(1/2)# is continuous at x=1/2?
• How do you prove that the function #f(x)=(x^2+7x+10)/(x+5) # is continuous everywhere but x=-5?
• How do you prove that the function #f(x)=(x-5)/ |x-5|# is continuous everywhere but x=5?
• How do you prove that the function #g(x) = x^3 / x# is continuous everywhere but x=0?
• 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 a =-1?
• How do you prove that the function #f(x) = x^2 -3x +5# is continuous at a =2?
• How do you prove that the function #f(x) = [x^2 + x] / [x]# is not continuous at a =0?
• How do you prove that the function #1/x# is continuous at x=1?
• How do you prove that the function #xsin(1/x)# is continuous at x=0?
• Question #12cba
• For a continuous function (let's say f(x)) at a point x=c, is f(c) the limit of the function as x tends to c? Please explain.
• Question #5b210
• Let f be a function so that (below). Which must be true? I. f is continuous at x=2 II. f is differentiable at x=2 III. The derivative of f is continuous at x=2 (A) I (B) II (C) I & II (D) I & III (E) II & III
• Is #f(x)=(x^2-9)/(x-3)# continuous at #x=3#?
• How do you prove by definition that the function #f(x)= x^2 sin (1/x)# is continuous at x=0?