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Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.?
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Continuity of the function f(x) = 1/x
To understand the continuity of the function f(x) = 1/x, we need to analyze its behavior at different points, particularly at x = 0, where the function is not defined.
Definition of continuity
- A function is said to be continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.
Analysis of f(x) = 1/x
- For x ≠ 0, the function f(x) = 1/x is well-defined and continuous since it is a basic rational function.
- However, at x = 0, the function is not defined as division by zero is undefined.
Limits at x = 0
- To determine the continuity at x = 0, we need to calculate the limit of f(x) as x approaches 0.
- The limit as x approaches 0 from the positive side is +∞, and from the negative side is -∞.
Conclusion
- Since the limit of f(x) as x approaches 0 does not exist (as it approaches different values from the positive and negative sides), the function f(x) = 1/x is not continuous at x = 0.
- Therefore, the function f(x) = 1/x is continuous for all x ≠ 0 but not at x = 0.
To understand the continuity of the function f(x) = 1/x, we need to analyze its behavior at different points, particularly at x = 0, where the function is not defined.
Definition of continuity
- A function is said to be continuous at a point if the limit of the function as x approaches that point exists and is equal to the value of the function at that point.
Analysis of f(x) = 1/x
- For x ≠ 0, the function f(x) = 1/x is well-defined and continuous since it is a basic rational function.
- However, at x = 0, the function is not defined as division by zero is undefined.
Limits at x = 0
- To determine the continuity at x = 0, we need to calculate the limit of f(x) as x approaches 0.
- The limit as x approaches 0 from the positive side is +∞, and from the negative side is -∞.
Conclusion
- Since the limit of f(x) as x approaches 0 does not exist (as it approaches different values from the positive and negative sides), the function f(x) = 1/x is not continuous at x = 0.
- Therefore, the function f(x) = 1/x is continuous for all x ≠ 0 but not at x = 0.
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Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.?
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Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.?.
Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Discuss the continuity of the function f defined by f(x)=1/x, x not qual to zero I didnt underdtand what ncert book has explained please help me with this.?.
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