If f(x) = { x^2, x < 3; k, x = 3; 2x, x > 3 } is continuous at x = 3, what is the value of k?
Practice Questions
1 question
Q1
If f(x) = { x^2, x < 3; k, x = 3; 2x, x > 3 } is continuous at x = 3, what is the value of k?
3
9
6
0
For continuity at x = 3, we need limit as x approaches 3 from left (9) to equal f(3) = k, thus k = 9.
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = { x^2, x < 3; k, x = 3; 2x, x > 3 } is continuous at x = 3, what is the value of k?
Solution: For continuity at x = 3, we need limit as x approaches 3 from left (9) to equal f(3) = k, thus k = 9.
Steps: 6
Step 1: Understand that the function f(x) has different expressions depending on the value of x.
Step 2: Identify the three parts of the function: f(x) = x^2 when x < 3, f(x) = k when x = 3, and f(x) = 2x when x > 3.
Step 3: For the function to be continuous at x = 3, the limit of f(x) as x approaches 3 from the left must equal f(3).
Step 4: Calculate the limit of f(x) as x approaches 3 from the left: since x < 3, use f(x) = x^2. So, limit as x approaches 3 from the left is 3^2 = 9.
