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Calculus - Limit Continuity And Differentiability Video Lecture | Engineering Mathematics - Civil Engineering (CE)
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FAQs on Calculus - Limit Continuity And Differentiability Video Lecture - Engineering Mathematics - Civil Engineering (CE)
| 1. What is the definition of a limit in calculus? |  |
Ans. In calculus, the limit of a function is the value that the function approaches as its input approaches a certain value. It represents the behavior of the function near a particular point and is denoted by the symbol lim.
| 2. How can I determine if a function is continuous? | |
Ans. A function is continuous if it is defined at every point within its domain and there are no breaks, jumps, or holes in its graph. Mathematically, a function f(x) is continuous at a point x=a if the limit of f(x) as x approaches a is equal to f(a) itself.
| 3. What does it mean for a function to be differentiable? | |
Ans. A function is said to be differentiable at a point if the derivative of the function exists at that point. Geometrically, it means that the function has a well-defined tangent line at that point, indicating how the function changes at that specific location.
| 4. Are all continuous functions differentiable? | |
Ans. No, not all continuous functions are differentiable. A function can be continuous without being differentiable if it has a sharp corner, vertical tangent, or a discontinuity in its graph. Differentiability requires not only continuity but also a smoothness property.
| 5. How can I find the derivative of a function? | |
Ans. To find the derivative of a function, you can apply differentiation rules such as the power rule, product rule, quotient rule, and chain rule. These rules allow you to find the rate of change or slope of the function at any point. The derivative represents the instantaneous rate of change of the function.
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Dec 25, 2024 Last updated |
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