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Comparing features of functions (example 1) Video Lecture - Engineering Mathematics

FAQs on Comparing features of functions (example 1) Video Lecture - Engineering Mathematics

1. What are some common features of functions in Engineering Mathematics?
Ans. Some common features of functions in Engineering Mathematics include domain and range, continuity, differentiability, and the presence of critical points.
2. How can I determine the domain and range of a function in Engineering Mathematics?
Ans. To determine the domain of a function, you need to identify the set of input values for which the function is defined. The range, on the other hand, refers to the set of all possible output values of the function. To find the range, you can analyze the behavior of the function and consider the limits of its values as the input approaches certain values.
3. What does it mean for a function to be continuous in Engineering Mathematics?
Ans. A function is said to be continuous if there are no breaks, jumps, or holes in its graph. This means that the function can be drawn without lifting the pen from the paper. Mathematically, a function is continuous if the limit of the function as the input approaches a specific value is equal to the value of the function at that point.
4. How do I determine if a function is differentiable?
Ans. A function is differentiable if it has a derivative at every point in its domain. To determine if a function is differentiable, you can check if it satisfies the conditions for differentiability, such as having a smooth and non-vertical graph, having a defined tangent line at each point, and having no sharp corners or cusps.
5. What are critical points in Engineering Mathematics?
Ans. Critical points of a function are the points where the derivative of the function is either zero or undefined. These points are significant as they can help in determining the maximum or minimum values of the function or the points of inflection. Critical points can be found by setting the derivative of the function equal to zero and solving for the corresponding input values.
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