Let f x cx if x 4 For what value of the constant c is the

Last updated: 1/17/2024

Let f x cx if x 4 For what value of the constant c is the function f continuous on 0 Step 1 Recall that function is continuous at a number a if the following holds lim f x f a x10 We are given the following F x 2x Cx 3x If x 4 x cx if x 4 We note that for all values of the constant c the function f is continuous on both 4 and 4 The only case that we need to consider is when x 4 For the function f to be continuous on we need to ensure that there is not a discontinuity To do so we must determine the value of c such that the following holds lim f x lim f x X 44 x 4 Find the following limits lim f x lim cx 3x x 4 X 4 lim f x lim x cx x st x 4