Calculating the Limit of {(e^h-1)/h} as h→0

• Ravi Mandavi
In summary, the limit of {(e^h-1)/h} as h approaches 0 is equal to 1 and can be solved using L'Hôpital's rule or by taking the limit of the function. Calculating this limit is important in mathematics and science, particularly in understanding the behavior of a function. It can be solved without calculus, but using calculus is often the most efficient method. The number e in the function is a fundamental constant in calculus and has real-world applications in various fields, such as physics, engineering, and economics.
Ravi Mandavi
how, limit h->0 {(e^h-1)/h}= 1?
Although this is not home work but i stuck on it

You can apply L'Hopital's Rule and it should work out.

1. What is the limit of {(e^h-1)/h} as h approaches 0?

The limit of {(e^h-1)/h} as h approaches 0 is equal to 1. This can be proven using L'Hôpital's rule or by taking the limit of the function as h approaches 0.

2. Why is it important to calculate the limit of {(e^h-1)/h} as h approaches 0?

Calculating the limit of {(e^h-1)/h} as h approaches 0 is important in many areas of mathematics and science, particularly in calculus and differential equations. It allows us to understand the behavior of a function as it approaches a specific point.

3. Can the limit of {(e^h-1)/h} as h approaches 0 be solved without using calculus?

Yes, the limit of {(e^h-1)/h} as h approaches 0 can also be solved using algebraic manipulation and the properties of limits. However, using calculus is often the most efficient and accurate method.

4. What is the significance of e in the function {(e^h-1)/h}?

The number e is a mathematical constant that is approximately equal to 2.71828. It is a fundamental constant in calculus and is often used in the study of exponential growth and decay.

5. Are there any real-world applications of calculating the limit of {(e^h-1)/h} as h approaches 0?

Yes, there are many real-world applications of calculating this limit, such as in physics, engineering, and economics. It is used to model and predict various phenomena, such as population growth, radioactive decay, and interest rates.

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