Question

Use the three conditions to show that function f(x)=2x^2 +3x - 1 is continuous at x=0 .​

Answer 1

To show that f(x) = 2x^2 + 3x - 1 is continuous at x=0, check if the three conditions for continuity are satisfied.

Step-by-step explanation:

To show that the function f(x) = 2x^2 + 3x - 1 is continuous at x=0, we need to check the three conditions:

1. Condition 1: The function is defined at x=0. In this case, f(0) = 2(0)^2 + 3(0) - 1 = -1.
2. Condition 2: The limit of the function as x approaches 0 exists. To find this limit, we can plug in 0 for x in the function and simplify: lim(x→0) f(x) = lim(x→0) 2x^2 + 3x - 1 = -1. Therefore, the limit exists.
3. Condition 3: The limit of the function as x approaches 0 is equal to the value of the function at x=0. Using the same calculation as before, we find that the limit equals -1, which is the same as f(0).

Since all three conditions are satisfied, we can conclude that the function f(x) = 2x^2 + 3x - 1 is continuous at x=0.