Is the function f(x) = sqrt(x) continuous at x = 0?
Practice Questions
1 question
Q1
Is the function f(x) = sqrt(x) continuous at x = 0?
Yes
No
Only from the right
Only from the left
The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.
Questions & Step-by-step Solutions
1 item
Q
Q: Is the function f(x) = sqrt(x) continuous at x = 0?
Solution: The function f(x) = sqrt(x) is continuous at x = 0 as it is defined and the limit exists.
Steps: 5
Step 1: Understand what it means for a function to be continuous at a point. A function is continuous at a point if three conditions are met: the function is defined at that point, the limit exists at that point, and the limit equals the function's value at that point.
Step 2: Check if the function f(x) = sqrt(x) is defined at x = 0. Calculate f(0): f(0) = sqrt(0) = 0. So, the function is defined at x = 0.
Step 3: Find the limit of f(x) as x approaches 0. Calculate the limit: lim (x -> 0) f(x) = lim (x -> 0) sqrt(x) = sqrt(0) = 0.
Step 4: Compare the limit with the function's value at x = 0. We found that lim (x -> 0) f(x) = 0 and f(0) = 0.
Step 5: Since the limit exists, the function is defined at x = 0, and the limit equals the function's value, we conclude that f(x) = sqrt(x) is continuous at x = 0.
