Question

For the function f, how would you remove the discontinuity? In other words, how would you define f(3) in order for f to be continuous at 3? f(x) = 4 - x² / (x⁴ - 3)

Answer 1

To remove the discontinuity and make the function f(x) = (4 - x²) / (x⁴ - 3) continuous at 3, you need to redefine f(3) so that it matches the limit of the function as x approaches 3.

Step-by-step explanation:

To remove the discontinuity and make the function f(x) = (4 - x²) / (x⁴ - 3) continuous at 3, we need to redefine f(3) so that it matches the limit of the function as x approaches 3. To find the limit, we substitute x = 3 into the function and simplify:

lim(x→3) f(x) = lim(x→3) (4 - x²) / (x⁴ - 3) = (4 - 3²) / (3⁴ - 3) = 1 / 78

Therefore, to make f continuous at 3, we define f(3) = 1 / 78.