For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x If the function is continuous, then what is the value of k ?

Step-by-step solution

For the function to be continuous at x = 0 , the left-hand limit must be equal to the right-hand limit and the value of the function at x = 0 . Left-hand limit at x = 0 is given by: _ x 0⁻ f(x) = _ x 0⁻ 4(5^x) = 4(5^0) = 4 Right-hand limit at x = 0 is given by: _ x 0⁺ f(x) = _ x 0⁺ (8k + x) = 8k + 0 = 8k Equating the left-hand limit and the right-hand limit: 8k = 4 k = 4 8 = 0.5 Answer: 0.5