For what value of the constants A and B is the function #f(x)=x^2+bx+1# continuous for all X if x < 5? Calculus Limits Continuous Functions 1 Answer Steve M Dec 9, 2016 #b# can be any real number Explanation: #f(x)=x^2+bx+1# is a polynomial and is continuous for all real numbers #x# and constants #b#. Hence #b# can be any real number. Answer link Related questions What are continuous functions? What facts about continuous functions should be proved? How do you use continuity to evaluate the limit #sin(x+sinx)# as x approaches pi? 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)? Given two graphs of piecewise functions f(x) and g(x), how do you know whether f[g(x)] and... 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)#... How do you show that the function #f(x)=1-sqrt(1-x^2)# is continuous on the interval [-1,1]? See all questions in Continuous Functions Impact of this question 2302 views around the world You can reuse this answer Creative Commons License