Continuous Functions - Page 3

Questions
  • Why the function is discontinuous at a=1 given #f(x)= 1-x^2# if x < 1 and #f(x)= 1/x# if #x >= 1#?
  • How do you find the intervals on which the function is continuous given #y = (2)/((x + 4)^2) + 8#?
  • How do you find the intervals on which the function is continuous given # y = ln(3x-1)#?
  • Is the function f(x) = secx continuous on the interval [-pi/2, pi/2]?
  • If #f(x)=(x^2+6x+8)/(x+2)# if x<-2 and #kx^2#if #x>= -2#, what value of k would make the function continuous at x=-2?
  • How do we find the values of k and m that makes function continue anywhere piecewise function of #(x^2) + 5# when x > 2, #m(x+3) + k# when #-1 < x <=2# and #2(x^3) + x + 7# when #x <=-1#?
  • How do you find the values of c and d that make the following function continuous for all x given #f(x) = 9x# if x<1, #f(x) = cx^2+d# if #1<=x<2# and #f(x) = 3x# if #x>=2#?
  • How do you find the constant a so that the function is continuous on the entire real line given #f(x)=4, #x <= -1#, ax +b, -1< x <1 and 6, #x>=1#?
  • Is the function #2x-x^2# continuous if 0 ≤ x ≤ 2?
  • #lim_(x->0)(tan x - x)/x^3 = # ?
  • What facts about continuous functions should be proved?
  • How do you find values of x for which the function #g(x) = (sin(x^20+5) )^{1/3}# is continuous?
  • How do you find values of x where the function #f(x)=sqrt(x^2 - 2x)# is continuous?
  • How do you use continuity to evaluate the limit sin(x+sinx)?
  • How do you find the intervals on which the function is continuous given # y = sqrt(5x + 9)#?
  • How do you find the interval notation to prove #f(x)= x/(sqrt(1-x^2))# is continuous?
  • How do you use continuity to evaluate the limit #(e^(x^2) - e^(-y^2)) / (x + y)# as #(xy)# approached #(1,1)#?
  • 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#?
  • How do you show the function is continuous at the given number a #f(x)=(x+2x^3)^4#, a=-1?
  • Verify Rolle theorem for function: f(x)= #x^3-6x^2+11x-6# in the interval [1,3] ?