What is the limit of f(x) = 1/x as x approaches 0 from the right?
Practice Questions
1 question
Q1
What is the limit of f(x) = 1/x as x approaches 0 from the right?
0
Infinity
1
Does not exist
As x approaches 0 from the right, f(x) approaches infinity, indicating a discontinuity at x = 0.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the limit of f(x) = 1/x as x approaches 0 from the right?
Solution: As x approaches 0 from the right, f(x) approaches infinity, indicating a discontinuity at x = 0.
Steps: 5
Step 1: Understand the function f(x) = 1/x. This means for any value of x, you take 1 and divide it by that value.
Step 2: Identify what 'approaching 0 from the right' means. This means we are looking at values of x that are very small but positive, like 0.1, 0.01, 0.001, etc.
Step 3: Calculate f(x) for these small positive values. For example, f(0.1) = 1/0.1 = 10, f(0.01) = 1/0.01 = 100, and f(0.001) = 1/0.001 = 1000.
Step 4: Observe the pattern. As x gets closer to 0 from the right, the value of f(x) gets larger and larger.
Step 5: Conclude that as x approaches 0 from the right, f(x) approaches infinity. This means there is no finite limit, and we say the limit is infinity.
